Question

use the graph to answer questions 5. 5. choose the function that represents the graph to the left. a. h(x)=2\sqrt{x - 4} b. h(x)=2\sqrt{x + 4} c. h(x)=2\sqrt{x}-4 d. h(x)=2\sqrt{x}+4 what transformations on the graph of f(x)=\sqrt{x} result in the graph of the given function? 6. g(x)=4\sqrt{x + 2} a. stretch vertically by a factor of 4 and translate left by 2 units. b. stretch horizontally by a factor of 4 and translate left by 2 units. c. translate up by 4 and left by 2 units. which of the following questions are true? select two that apply. 7. a. x^{\frac{2}{7}}=\sqrt7{x^{2}} b. x^{\frac{4}{5}}=\sqrt{x^{9}} c. (x^{\frac{1}{2}})^{5}=\sqrt{x^{5}} d. (\sqrt{x^{3}})^{8}=x^{\frac{8}{3}} learning goal from 11.1 i can describe the relationship between rational exponents and radicals. lesson reflection (circle one) starting... getting there... got it!

Explanation:

Step1: Analyze question 5

The graph of $y = \sqrt{x}$ has a starting - point at $(0,0)$. The given graph has a starting - point at $(0, - 4)$. The general form of a square - root function transformation is $y=a\sqrt{x - h}+k$, where $(h,k)$ is the vertex. For the function $y = 2\sqrt{x}-4$, when $x = 0$, $y=-4$.

Step2: Analyze question 6

For the function $g(x)=4\sqrt{x + 2}$, compared to $f(x)=\sqrt{x}$, the coefficient 4 in front of the square - root function causes a vertical stretch by a factor of 4, and the $x+2$ inside the square - root function causes a left - shift of 2 units.

Step3: Analyze question 7

Recall the rule $x^{\frac{m}{n}}=\sqrt[n]{x^{m}}$.

• For option A: $x^{\frac{2}{7}}=\sqrt[7]{x^{2}}$, which is correct.
• For option B: $x^{\frac{4}{5}}=\sqrt[5]{x^{4}}

eq\sqrt{x^{9}}$.

• For option C: $(x^{\frac{1}{2}})^{5}=x^{\frac{5}{2}}=\sqrt{x^{5}}$, which is correct.
• For option D: $(\sqrt{x^{3}})^{8}=(x^{\frac{3}{2}})^{8}=x^{12}

eq x^{\frac{8}{3}}$.

Answer:

1. C. $h(x)=2\sqrt{x}-4$
2. A. Stretch vertically by a factor of 4 and translate left by 2 units.
3. A. $x^{\frac{2}{7}}=\sqrt[7]{x^{2}}$, C. $(x^{\frac{1}{2}})^{5}=\sqrt{x^{5}}$