Analysis
Grenzwerte, Ableitungen, Optimierung und Funktionsverhalten.
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10. the graph at the right shows $f(x) = 2(x - 3)^2 - 1$. a) evaluate $…
For part (a), \( f(-2)=49 \) ### Part (b)
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we have learned that 60% of the general population’s purchases are due …
A specific example: Last year, a brand advertised a limited-edition sneaker as a "never-to-be-restocked" item, with social media posts showing peers posting about their purchases.…
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modeling real life the amount y (in dollars) of money in your savings a…
To graph the linear equation \( y = 12.5x + 100 \), we can use the slope - intercept form of a linear equation \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - in…
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open-ended question take a look at the next one. try it on your own and…
To find \( f(-3) \), we need the definition of the function \( f(x) \). Since the function's equation or graph (which is partially visible) isn't fully provided, we can't calculat…
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what is the primary purpose of the constitutional amendment process? to…
To provide a mechanism for changing the Constitution
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solve the following system of equations graphically on the set of axes …
The solution is \((-4, 4)\)
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y ≥ -5x - 4
To graph \( y \geq -5x - 4 \): 1. Plot the y - intercept at \( (0, - 4) \) and use the slope \( - 5 \) to find another point (e.g., \( (-1, 1) \)). 2. Draw a solid line through th…
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evaluate the following functions. you get unlimited reattempts. $f(x) =…
\(-300\)
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evaluate the following functions you get unlimited reattempts. $f(x) = …
\(-54\)
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evaluate the following functions. you get unlimited reattempts. $f(x) =…
\( 77 \)
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evaluate the following functions. you get unlimited reattempts. $f(x) =…
\(-67\)
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find the slope between the given points 8. (-4, -1) and (-2, -5)
$-2$
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which functions are symmetric about the y - axis? check all of the boxe…
Check the boxes for the **first graph (top)** and **third graph (bottom)**.
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graph this line: y - 2 = -4(x - 1) click to select points on the graph.…
To graph the line \(y - 2=-4(x - 1)\): 1. Plot the point \((1,2)\) (from the point - slope form \(y - y_1=m(x - x_1)\) where \(x_1 = 1,y_1=2\)). 2. Use the slope \(m=-4\) (rise/ru…
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graph the system of equations. y = 2x + 2 y = x
To graph the system: - For \( y = 2x+2 \): Plot the points \( (0,2) \), \( (1,4) \), \( (-1,0) \) and draw a straight line through them. - For \( y = x \): Plot the points \( (0,0…
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question a quadratic function ( f(x) ) is hidden from view. you must fi…
$(-1, 5)$
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736,560 ÷ \\boxed{} = 736.56
\( 1000 \)
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you need to create a legal structure for your small business. you would…
D. S - Corporation
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select form to find quadratic feature question a quadratic function f(x…
The maximum value of $f(x)$ is $3$, and the most efficient form to use is Vertex Form.
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select form to find quadratic feature score: 0/3 penalty: none question…
$(1, \infty)$
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problem 8 determine the quotient of $33.8 \\div 32.5$.
\(1.04\)
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use long division to calculate the quotient. use the sketch tool or pap…
\(249.75\)
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use long division to calculate the quotient. use the sketch tool or pap…
\(352\)
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solve (8.5)·(-3)=a. a = (lesson 5-15)
\(-25.5\)
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evaluating piecewise functions algebraically. $f(x) = \\begin{cases} -\…
$2f(-4)=10$ $3f(0)=3$ $f(3)=3$ $f(1)$ is undefined (not in any domain interval)
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current skill $ multiply: \\frac{1}{5} * 3 provide an answer as a simpl…
$\frac{3}{5}$
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a car is traveling at a speed of either 55 miles per hour or 35 miles p…
The car spends $\frac{45}{22}$ hours (approximately 2.05 hours) traveling at 55 miles per hour.
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worksheet solving systems of equations by graphing name date solve each…
s: 1. Intersection: \( \boldsymbol{(1, -1)} \) 2. Intersection: \( \boldsymbol{(3, -4)} \) 3. Intersection: \( \boldsymbol{(3, -2)} \) 4. Intersection: \( \boldsymbol{(-1, -3)} \)
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question graph the equation shown below by transforming the graph of th…
The graph of $y=-\sqrt{x}$ is the reflection of $y=\sqrt{x}$ over the x-axis, passing through the points $(0,0)$, $(1,-1)$, $(4,-2)$, $(9,-3)$ with a smooth curve extending to the…
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the graphs of functions f and g are shown. function g is defined as $g(…
2
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type the correct answer in each box. use numerals instead of words. con…
$h(0) = 10$ $h(4) = 16$
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select the correct answer. which function has an asymptote at x = 5 and…
A. $f(x) = \log(x - 5)$
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you might need: calculator what is the slope of the line?
\(-2\)
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atch each transformation of function f to a feature of the transformed …
$j(x) = f(x + 2)$ → y-intercept at $(0, 2)$ $m(x) = -f(x)$ → function decreases as x increases $h(x) = f(x) + 2$ → asymptote of $y = 2$ $g(x) = 2f(x)$ → y-intercept at $(0, 4)$
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select the correct answer. what is the y-intercept of $f(x) = 3^{x + 2}…
B. (0,9)
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what is the y-intercept of function g if $g(x) = -4f(x) + 12$? a. $(0,8…
A. $(0, 8)$
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which statements describe key features of function f?range of {y| 0 < y…
- range of $\{y|0 < y < \infty\}$ - y-intercept at $(0, 1)$ - horizontal asymptote of $y = 0$
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a. $f(x) = \\begin{cases} -5, & x \\leq -2 \\\\ x^2 + 5, & -2 < x < 1 \…
B. $f(x) = \begin{cases} 5, & x \leq -2 \\ x^2 - 5, & -2 < x < 1 \\ 2^{(x-2)} - 3, & x \geq 1 \end{cases}$
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select the correct answer. consider function ( f(x) = \begin{cases} 2^x…
B. As $x$ approaches positive infinity, $f(x)$ approaches positive infinity.
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post test: exponential and logarithmic functions which inequality repre…
B. $x \geq -1$
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select the correct answer. what is the solution to this equation? $8(e)…
B. $x = \frac{\ln(0.5) - 1}{2}$
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select the correct answer. what is the approximate value of this logari…
C. 1.53
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select the correct answer. over which interval of the domain is functio…
B. The function is increasing only.
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select the correct answer. what is the value of \\( g(-4) \\)? \\( g(x)…
D. 1
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select the correct answer. what is the equation of the asymptote for th…
A. $x = 0$
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which is a feature of function g if $g(x) = -f(x - 4)$? a. $y$-intercep…
D. x-intercept at $(5, 0)$
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transformation of function f with a feature of the transformed function…
# Explanation: ## Step1: Analyze $j(x)=f(x+3)$ transformation The graph of $f(x)$ shifts left 3 units. - The original function $f(x)$ has a vertical asymptote at $x=-2$ (from the …
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match each transformation of function f with a feature of the transform…
$h(x) = 3f(x) - 3$ $\boldsymbol{\longrightarrow}$ vertex at $(2, 0)$ $j(x) = f(x + 3)$ $\boldsymbol{\longrightarrow}$ domain of $(-2, \infty)$ $g(x) = -f(x - 3)$ $\boldsymbol{\lon…
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over what interval of the domain is function f positive? a. \\((2, \\in…
B. $(3, \infty)$
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the asymptote of the function is \\(\\boldsymbol{x = 2}\\)\\(\\boldsymb…
The asymptote of the function is $\boldsymbol{x=3}$. For very high x-values, $\boldsymbol{y \text{ approaches positive infinity (increases without bound)}}$
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graph w\ graph x\ graph y\ graph z\ complete this statement given th\\(…
The graph of function \(g\) is graph **Y** because the graph of function \(g\) is the result of a **reflection across the x-axis** applied to function \(f\).
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select all the correct answers. consider the parent function $f(x)=e^x$…
- y-intercept - range - horizontal asymptote - end behavior
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to produce g, function f was reflected over the x - axis and shifted up…
$g(x) = -f(x) + 5$
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to produce g, function f was reflected over the x - axis and shifted up…
First dropdown: shifted up 5 units Second dropdown: $g(x) = -2^x + 5$
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select all the correct answers. which expressions are equivalent to \\b…
- $\boldsymbol{\log 10}$ - $\boldsymbol{1}$
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select the correct answer. what is the approximate value of this logari…
B. 1.80
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select the correct answer from each drop - down menu. for all positive …
For all positive values of $x$, the value of $\log_x x$ is always $\boldsymbol{1}$, and the value of $\log_x 1$ is always $\boldsymbol{0}$.
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if ( f(x)=sqrt{x} ), which equation describes the graphed function? a. …
C. \( y = - f(x)-3 \)
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the parent function $f(x) = x^3$ is represented by graph a. graph a is …
Graph B: \( \boldsymbol{x^3 - 2} \) Graph C: \( \boldsymbol{2x^3+2} \) (Note: The answer is based on the analysis of vertical shifts and stretches for the cubic function transform…
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the parent function $f(x) = x^3$ is represented by graph a. graph a is …
Graph B: \( g(x) = (x - 1)^3 - 2 \) Graph C: \( h(x) = 2x^3 \)
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type the correct answer in each box. use numerals instead of words. wha…
The first box is \( 4 \), the second box is \( 3 \), and the third box is \( 0 \). So \( f^{-1}(x)=\boldsymbol{4}x^{2}-\boldsymbol{3} \), for \( x\leq\boldsymbol{0} \)
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select the correct answer. which function is the inverse of $f(x) = -x^…
B. \( f^{-1}(x) = \sqrt[3]{-x - 9} \)
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select the correct answer. consider these functions: f(x) = x + 1, g(x)…
C. \(\frac{2}{x} + 1\)
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f(x) = -8x⁵ + 4x³ + 5x a. function f is both even and odd. b. function …
D. Function \( f \) is odd.
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select the correct answer. consider functions f and g. f(x) = 3√x + 1 c…
C. 1
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select the correct answer. each statement describes a transformation of…
D. It is the graph of \( f \) translated 3 units up and 7 units to the right.
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select the correct answer. which function has a domain of all real numb…
D. \( y = (2x)^{\frac{1}{3}}-7 \)
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part 1: key background information directions: use the reading to fill …
s: 1. judicial 2. John Adams; Judiciary 3. fifteen 4. Senate; Thomas Jefferson
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an object was launched off the top of a building. the function $f(x) = …
$f(-1) = 0$, meaning that -1 seconds after the object was launched, the object was 0 feet above the ground. This interpretation is not meaningful in the context of the problem. $f…
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the graph of $f(x) = \\frac{1}{x}$ is given below. write the equation o…
\( g(x)=\frac{1}{x}-2 \)
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what does it mean to raise a number to the power of 0? you can look at …
\(1\)
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given the function $h(x) = x^2 + 9x + 14$, determine the average rate o…
1
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question the function ( y = f(x) ) is graphed below. what is the averag…
\(-1\)
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question graph the following function on the axes provided. $f(x)=\\beg…
The graph consists of a horizontal line segment \( y = -1 \) from \( x = -4 \) (open) to \( x = 1 \) (open), and a line segment \( y = x + 2 \) from \( x = 1 \) (open) to \( x = 5…
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what is the domain of the function $y = \\sqrt3{x}$?\ $\\bigcirc$ $-\\i…
\( -\infty < x < \infty \)
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write \\(\frac{175}{100}\\) as a decimal \\(\frac{7}{4} \\times 1 = \fr…
1.75
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type the correct answer in the box. use numbers instead of words. enter…
-4.25
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based on the diagram, pick the two choices below that represent the exp…
\(\sin(19^{\circ})\), \(\frac{12}{37}\)
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find the average rate of change of $h(x)=x^2 - 5x + 2$ from $x = 2$ to …
2
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use the interactive graph below to sketch a graph of $y = 3\\log_2(-x) …
1. Vertical Asymptote: $x=0$ (the y-axis) 2. Key points to plot: $(-1, -9)$, $(-2, -6)$ (or $(-4, -3)$) 3. The graph is a reflected (over y-axis), vertically stretched (by factor …
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divide. $1\\frac{1}{3}\\div\\frac{5}{6}=$ submit
\(\frac{8}{5}\) (or \(1\frac{3}{5}\))
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solve this system of equations: y = x - 4 y = 6x - 10
The solution is \( x = \frac{6}{5} \), \( y = -\frac{14}{5} \) (or \( x = 1.2 \), \( y = -2.8 \)).
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give a rule of the piecewise - defined function. give the domain and th…
- **Rule**: Option A: \( f(x)=\begin{cases}3& \text{if }x < - 1\\-2& \text{if }x > 2\end{cases}\) - **Domain**: \( (-\infty,-1)\cup(2,\infty)\) (Option B) - **Range**: \(\{ - 2,3\…
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what does the transformation $f(x) \\mapsto f(x + 4)$ do to the graph o…
translates it 4 units left
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score on last try: 0 of 1 pt. see details for more. next question get a…
The graph of $g(x)=\sqrt{x}+1$ is the graph of $f(x)=\sqrt{x}$ shifted vertically upward by 1 unit, passing through the points $(0,1)$, $(1,2)$, and $(4,3)$.
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both of these functions grow as x gets larger and larger. which functio…
The function $f(x)=\frac{1}{2}(5)^x$ (or $f(x)$) eventually exceeds $g(x)=6x + 2$ (or $g(x)$).
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score on last try: 0 of 1 pt. see details for more. next question get a…
$g(x) = -3(x-2)^2 - 3$
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the graph of $y = f(x)$ is shown below. find all values of $x$ where $f…
$x=0$ and $x=4$
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graph this line: $y - 7 = 2(x - 2)$ click to select points on the graph.
Plot the points $(2, 7)$, $(0, 3)$, and/or $(1, 5)$, then draw a straight line passing through them. The line has a slope of 2 and y-intercept at $(0, 3)$.
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approximate \\(\\sqrt{88}\\) by following the steps below.\\(\\sqrt{88}…
\(9.38\) and \(9.39\)
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solve the exponential equation. express the solution in terms of natura…
In terms of logarithms: $\{\log 4.23\}$ Decimal approximation: $\{0.63\}$
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complete the table. $f(x)=x^3$ | $x$ | $f(x)$ | | --- | --- | | $-3$ | …
| $x$ | $f(x)$ | |-----|--------| | $-3$ | $9$ | | $-1$ | $1$ | | $1$ | $1$ | | $3$ | $9$ |
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a quadratic function $y = f(x)$ is plotted on a graph and the vertex of…
The vertex of \( g(x) \) is \( (6, - 4) \)
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write your answer in the form $a|x - h| + k$, where $a$, $h$, and $k$ a…
$g(x) = -|x| - 8$
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graph this line using the slope and y-intercept: $y = \\frac{9}{8}x$ cl…
The line passes through the points $(0,0)$ and $(8,9)$, and extends infinitely in both directions along the grid.
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representing a graph with a slope-intercept equation a function f(x) is…
Slope: $m=2$ y-intercept: $b=1$ Equation: $y=2x+1$
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determine the domain on which the following function is decreasing.
$(-\infty, -4)$
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fill in the missing number. \\(\frac{1}{2} \times \frac{2}{3} = \frac{s…
1
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graph the function $f(x) = 2\\log_4(x + 5)$ on the axes below. you must…
The vertical asymptote is \( x = - 5 \). Two points with integer coordinates are \( (-4,0) \) and \( (-1,2) \) (you can plot these on the graph along with the vertical asymptote \…
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graph the function $f(x) = -3(3)^{x - 3}$ on the axes below. you must p…
Asymptote: \( y = 0 \) Two points with integer coordinates: \( (3, -3) \) and \( (4, -9) \) (or other valid integer coordinate points like \( (2, -1) \) and \( (3, -3) \))