微积分
极限、导数、最优化与函数性质。
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directions: analyze the graphs, and solve the linear equation questions…
The system of equations is: $$ \begin{cases} y = 4x \\ y = 2x + 10 \end{cases} $$
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after taking 10 consecutive hours off - duty, what are the maximum limi…
B. 11 hours of driving within a 14 - hour on - duty window
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given the following exponential function, identify whether the change r…
Growth, 2% increase
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16) \\( y = -7x + 6 \\)\\( y = 4x - 16 \\)
The solution is \(x = 2\), \(y=-8\) (or the ordered pair \((2,-8)\)).
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quadratic function f can be written as $f(x)=(x - 7)^2+1$ and $f(x)=x^2…
\(-14\)
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given the following exponential function, identify whether the change r…
Decay, 50.8% decrease
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in the text, you read this about states rights in the confederacy: the …
C. The Confederate military had difficulty organizing itself
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in the text, you read this about states’ rights in the confederacy: the…
B. sectionalism
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graph the following function. state the domain and range. is the functi…
## Domain: The domain of \( h(x)=\sqrt[3]{x}-4 \) is all real numbers. In interval notation, the domain is \( (-\infty,\infty) \). ## Range: The range of \( h(x)=\sqrt[3]{x}-4 \) …
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given the following exponential function, identify whether the change r…
Growth, 1% increase
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a committee must be formed with 4 teachers and 7 students. if there are…
171600
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30. this excerpt is from a document written in the late 1700s. and, whe…
A. It outlined the process for creating new states.
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defining the limits of student speech while protecting the students in …
- **Strengthening Credibility**: Acknowledging limits shows the Court is reasonable, balancing free speech with school needs (order, rights protection), avoiding an extreme “all -…
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how can a table of values be created in order to graph a logarithmic fu…
A. Rewrite the logarithm in exponential form and plug in the \( y \)-values.
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20. the 14th amendment guarantees — a. voting rights b. equal protectio…
20. B. Equal protection under the law 21. B. Separate but equal 22. C. Segregation in schools is unequal 23. B. Marbury v. Madison 24. B. Equal protection in recounts 25. B. Unlim…
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35. which argument was made by anti - federalists such as patrick henry…
B. The Constitution needs to outline individual rights that are to be protected.
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given the function $f(x) = \\log_7 x$, which of the following functions…
\( g(x)=-8\log_7(x + 5)-9 \) (the first option)
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which of the following correctly identifies the transformation of $f(x)…
A. horizontal shift left 7 units
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which inequality is represented by the graph? $\\circ$ $y > -\\frac{2}{…
A. $y > -\frac{2}{3}x+1$
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which of the graphed functions is continuous?
The top-left graphed function (the V-shaped graph with a closed point at the origin, no gaps or jumps) is continuous.
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which of the following describes the graph of $y = \\sqrt{-4x - 36}$ co…
stretched by a factor of 2, reflected over the \(y\)-axis, and translated 9 units left (the last option: "stretched by a factor of 2, reflected over the \(y\)-axis, and translated…
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given the following exponential function, identify whether the change r…
Growth, 9% increase
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which of the graphed functions has a removable discontinuity?
The bottom-left graphed function (with points \((3,2)\), \((5,2)\), \((3,-1)\), \((5,-1)\) and a hole at \((3,1)\)) has a removable discontinuity.
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piecewise defined functions removing discontinuities which statement is…
You can remove the discontinuity at $x = 0$ by defining $g(0) = 0$.
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question 7 given ( f(x) = -3x^2 - x - 15 ), find ( f(-8) )
\( -199 \)
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11. complete the table with three ways you can deposit money into your …
One advantage is that credit unions often offer lower fees (e.g., no monthly service fees) and better interest rates on checking accounts because they are member - owned and prior…
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which statement is true for ( g(x) ) shown in the graph? you can remove…
You can remove the discontinuity at $x = 0$ by defining $g(0) = 2$.
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what is the domain of the function $y = \\sqrt{x}$?\ $\\bigcirc$ $-\\in…
\( 0\leq x < \infty \) (the third option)
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how does the graph of $y = \\sqrt{x} + 2$ compare to the graph of the p…
The graph is a vertical shift of the parent function 2 units up.
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the range of which function includes -4? ○ $y = \\sqrt{x} - 5$ ○ $y = \…
\( y=\sqrt{x}-5 \) (the first option)
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evaluate (7 - 4) × 3.
9
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evaluate $3 + (2 \\times 5)$.
13
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b. find the inverse function. c(n) = 50 + 4n c^{-1}(n) = \\frac{n - 50}…
The inverse function is \( \boldsymbol{C^{-1}(n)=\frac{n - 50}{4}} \) ### Part c: What information does the inverse function give us?
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6. this map shows the land gained by the united states in the mexican c…
Figuring out how to balance free and slave states
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b. find the inverse function. c(n) = 50 + 4n
The inverse function is \( c^{-1}(n)=\frac{n - 50}{4} \) (or \( c^{-1}(n)=\frac{1}{4}n - \frac{25}{2} \))
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b. find the inverse function. \\( c(n) = 50 + 4n \\)
La función inversa es \( \boldsymbol{C^{-1}(n) = \frac{n - 50}{4}} \) (o también se puede escribir como \( C^{-1}(n) = \frac{1}{4}n - \frac{25}{2} \) al simplificar la fracción).
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3.1.2 discuss & practice directions: think about the following question…
### Similarities: - All are smooth, continuous, and model variable relationships. ### Differences: - **Shape**: Linear = straight line; Quadratic = parabola; Exponential = curve. …
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answer attempt 1 out of 3 domain of function: range of function: the fu…
# Explanation: ## Step1: Analyze the graph's symmetry or repeated y - values Looking at the graph, we can see that the function is a parabola - like (but piece - wise) curve. For …
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graph the following function. state the domain and range. is the functi…
- Correct graph: Option A (assuming the visual of Option A matches the graph of \(y = \sqrt[3]{x-8}\) which is an increasing cube - root function shifted right by 8 units). - Doma…
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given the following exponential function, identify whether the change r…
The function represents decay with a percentage rate of decrease of \( 95\% \).
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philadelphia nativist riots of 1844 - rioters burned the property of ir…
A. The Constitution protects religious freedom, but individuals sometimes violate the religious rights of others.
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given the following exponential function, identify whether the change r…
The function represents growth with a percentage rate of increase of \( 98\% \).
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you can remove the discontinuity at ( x = 3 ) by defining ( g(3) = -1 )…
- You can remove the discontinuity at $x=3$ by defining $g(3)=-1$. - You can remove the discontinuity at $x=0$ by defining $g(0)=2$.
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what does it mean to raise a number to the power of 0? you can look at …
\(9\)
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complete the definition of h(x) so that it is continuous over its domai…
$a = 0$ $b = 2$
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select the correct text in the passage. which sentence should be includ…
(Assuming the correct option is, for example) "Michelangelo's life was characterized by ceaseless study, unwavering devotion to art, and a lifelong pursuit of learning, as evidenc…
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9. which quadratic function does the graph represent? a) $f(x) = -x^2 +…
a) \( f(x) = -x^2 + 6x + 7 \) ### Problem 10 (Vertex Form of Parabola)
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the lincoln and congressional republican plans differed. read each quot…
To solve this, we analyze each quote based on the key differences between the Congressional Reconstruction Plan (more stringent, focused on civil rights for freedmen, higher requi…
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origami is the traditional japanese art of paper folding. as an introdu…
The number of layers increases by a factor of 2 for each additional fold.
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which function is represented by the graph below? $y = \\frac{1}{2}x - …
$y=2x-4$
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for the following rational functions, find a.) \\(\\lim_{x\\to\\infty} …
a.) $\boldsymbol{+\infty}$ b.) $\boldsymbol{-\infty}$ c.) No horizontal asymptote exists. --- ### For 13.) $f(x) = \frac{2x^3+10x^2+12x}{x^4+2x^3}$
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what is the slope of the line that passes through the points (3, 8) and…
$-1$
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4. here is the graph that represents a function. which one equation rep…
D. \( j(x) = |x| + 1 \)
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value of this expres operations in the c 8 - 3·9 enter your answer press
-19
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what is the domain of the graph shown? $(-infty, 4)$ $(0, 4)$ $(-4, 4)$…
$(-\infty, \infty)$
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hese numbers. -84 - 67 u enter your answer press g
\(-151\)
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which rule describes the function whose graph is shown? $f(x)=\\begin{c…
$g(x)=\begin{cases} x + 6, & x < -2 \\ x^2, & -2 \leq x < 2 \\ 6 - x, & x \geq 2 \end{cases}$
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-41 + (-9)
\( -50 \)
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k. \\(\\frac{3\\sqrt{5}}{\\sqrt{2}}\\) 1. \\(\\frac{1}{\\sqrt{3}}\\)
- For \( \frac{3\sqrt{5}}{\sqrt{2}} \): \( \frac{3\sqrt{10}}{2} \) - For \( \frac{1}{\sqrt{3}} \): \( \frac{\sqrt{3}}{3} \)
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evaluate the function for the indicated values $f(x)= \\begin{cases} 2x…
$f(-10) = -19$ $f(2) = 4$ $f(-5) = -9$ $f(-1) = 1$ $f(8) = -5$
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alcos ailnq.1,13, ail3.17, 18, 20, 20a lesson 3.1 graphing quadratic fu…
To analyze the key features of the quadratic function \( f(x) = -2x^2 - 4x + 6 \), we can follow these steps: ### Step 1: Determine the direction of the parabola The coefficient o…
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use the graph to determine a. the function’s domain; b. the function’s …
a. Domain: $[0, 16]$ b. Range: $[0, 6]$ c. x-intercept: $(16, 0)$ d. y-intercept: $(0, 6)$ e. $f(16)=0$
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evaluate the end behavior of the function $f(x) = \\frac{x^5 + 2x - 13}…
1. As $x \to 0^-$, $f(x) \to \infty$ 2. As $x \to 0^+$, $f(x) \to -\infty$
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math practice name warm - up find the slope of each line. 1) 2) 3) 4) 5…
1. $\frac{1}{4}$ 2. $-\frac{1}{3}$ 3. $\frac{1}{3}$ 4. $-\frac{1}{2}$ 5. $0$ 6. $3$ 7. $-\frac{3}{2}$ 8. Undefined
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consider the rational function $f(x) = \\frac{x^2 - 1}{x^2 - 4}$. which…
1. The function has a horizontal asymptote at $y = 0$. 2. The function has a removable discontinuity at $x = -3$.
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11 the graph of the function ( g ) is shown on the following grid. whic…
B
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practice questions - rational functions: asymptotes & function behavior…
As \( x\to-\infty \), \( g(x)\to\infty \); As \( x\to\infty \), \( g(x)\to1 \) So the first blank: \( \infty \), the second blank: 1
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| | congressional reconstruction plan | lincoln reconstruction plan | |…
To solve this, we analyze the key differences between the Congressional Reconstruction Plan (more strict, punitive, focused on civil rights for freedmen) and Lincoln's Reconstruct…
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quadratic function $f(x) = ax^2 + bx + c$, where $a \ eq 0$ | x | y | |…
If it's the axis of symmetry (x - coordinate of vertex): \( \boldsymbol{-\frac{b}{2a}}\) If it's the roots of the quadratic equation \( ax^{2}+bx + c = 0\): \( \boldsymbol{\frac{-…
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show steps to solve. 8) find the inverse of the function ( f(x) = sqrt{…
The inverse function is \( f^{-1}(x)=(x + 13)^2 \), where \( x\geq - 13 \)
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13. \\log_{\\square} 36 = 2 \\square = \\square 14. find the inverse of…
13. $6=6$ 14. $\log_{0.3}x$ (or $\frac{\ln x}{\ln 0.3}$) 15. $2^x$
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select the functio f(x)=\\sqrt{x + 4} and check the show values box. us…
Part 1: A. $f(0)=2$ Part 2: A. $f(-3)=1$ Part 3: B. $f(-6)$ has no value
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quadratic function $f(x) = ax^2 + bx + c$, where $a \ eq 0$
To determine the parts of the quadratic function \( f(x) = ax^2 + bx + c \) (where \( a eq 0 \)): ### Step 1: Identify the coefficient of \( x^2 \) The term \( ax^2 \) has \( a …
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select the functio f(x)=√(x + 4) and check the show values box. use th …
Part 1: A. $f(0)=2$ Part 2: A. $f(-3)=1$
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select the function f(x)=\\sqrt{x + 4} and check the show values box. u…
A. $f(0)=2$
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select the function f(x)=x²−5. check the show values and integer x - va…
A. The value(s) of x when f(x)=4 is/are $\{3, -3\}$.
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in sentence 8 (reproduced below), the writer wants to limit the scope o…
D. Changing "the general public" to "people without gastrointestinal disorders"
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show steps to solve. 6) find the inverse of the function ( f(x) = \frac…
The inverse function is \( f^{-1}(x)=4x + 24 \)
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identify the range for the function, f(x). $(-infty, infty)$ $(-infty, …
$(-2, \infty)$
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cms 2025-2026 nc math 4 initial credit (approved for wmhs spr 26) piece…
$(-\infty,-2)\cup(-2,0)\cup(0,\infty)$
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question 52 of 60 add. write your answer as a mixed number in simplest …
\(8\frac{13}{20}\) ### Question 53:
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a. \\(\\sqrt{324}\\) b. \\(\\sqrt{864}\\)
\( 18 \) ### Part b
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describe cultural expression during the weimar republic. cultural expre…
1. Increase in arts, sciences, literature, and social theory 2. United States
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11. simplify the expression. \\log_{7}7^{-3x}=\\square
$-3x$
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tx fines & limits what is the established legal limit for blood alcohol…
0.08%
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use the functions below. - $f(x) = \\sqrt3{x}+2$ - $g(x) = 8x^3$ what i…
The correct option is the one where \((f\cdot g)(x)\) has the correct product (even if mis - written) and domain \((-\infty,\infty)\). Based on the domain (since the cube root fun…
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bellringer 1. $6\\frac{1}{2}+4\\frac{2}{5}$ 2. $2\\frac{3}{4}\\times\\f…
1. $10\frac{9}{10}$ 2. $1\frac{5}{6}$ 3. $5\frac{1}{2}$ 4. $2$
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10. use logarithms to solve the exponential equation. $e^{2x}=6$ the so…
$0.896$ --- ### Problem 11
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if $f(x) = \\sqrt3{2x + 1}$, which of the following tables shows values…
D. | x | \( f^{-1}(x) \) | |----|----------------| | -1 | -1 | | 0 | -0.5 | | 1 | 0 | | 2 | 3.5 | | 3 | 13 |
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9. use logarithms to solve the exponential equation. $4^{1 - 8x}=5^{x +…
$-0.525$
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8. solve for x. $2^x = 25$ solve for x. \\(\\bigcirc\\) a. \\(x = \\box…
A. $x = 4.6439$
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question given the following exponential function, identify whether the…
The function represents growth with a percentage rate of increase of \( 9\% \).
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6 the quadratic function ( f ) is represented by the equation, and the …
A. The y-intercept of $g(x)$ is greater than the y-intercept of $f(x)$. C. The x-coordinate of the vertex of $g(x)$ is greater than the x-coordinate of the vertex of $f(x)$. F. Th…
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write an exponential function in the form $y = ab^x$ that goes through …
$y=15(9)^x$
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this question has two parts. the equation of a quadratic function is gi…
Part A: $x=2$ Part B: $(2, -3)$
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1. solve the logarithmic equation.\\(\\log_{4}(3x - 2)=3\\)\ select the…
A. The solution is x=22.
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date: course: math 120 spring 2006 section 8011 assignment: 1. solve th…
A. The solution is $x=22$
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10. $f(x) = \\begin{cases} 2x + 5 & \\text{if } x < -4 \\\\ x^2 + 3x & …
\( \boldsymbol{-5} \) If the question was to find \( f(-4) \):
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10 in coordinate notation: match the correct transformation compared to…
## Part A: B. $(x,y)\to(x-3,3y+5)$ ## Part B: - Vertical stretch by a scale factor of 3 - Horizontal shift 3 units to the right - Vertical shift 5 units up (Vertex of $g(x)$ is $(…
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y = 2x - 1\ y = -3x - 6
$x=-1$, $y=-3$