Question

question 15 (5 points)

the table shows the cost of some apples. which function \\(f(x)\\) is represented in the table?

a) \\(f(x) = 2x + 2\\)
b) \\(f(x) = 0.5x + 2\\)
c) \\(f(x) = 0.5x\\)
d) \\(f(x) = 2x\\)

question 16 (5 points)

the function \\(f(x) = \sqrt5{x}\\) is translated 3 units in the negative \\(y\\)-direction and 8 units in the negative \\(x\\)-direction. select the correct equation for the resulting function.

a) \\(f(x) = \sqrt5{x + 8} - 3\\)
b) \\(f(x) = \sqrt5{x - 8} - 3\\)
c) \\(f(x) = \sqrt5{x + 3} - 8\\)
d) \\(f(x) = \sqrt5{x - 3} + 8\\)

Explanation:

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<reasoning>

Find the slope of the linear function

Using the Linear Modeling knowledge point
\[
m = \frac{f(2) - f(1)}{2 - 1} = \frac{4 - 2}{1} = 2
\]

Determine the linear equation

Using the Linear Modeling knowledge point
\[

$$\begin{aligned} &f(x) - 2 = 2(x - 1) \\ &f(x) = 2x \end{aligned}$$

\]

Apply horizontal translation

Using the Function Transformations knowledge point
\[
x \to x - (-8) = x + 8
\]

Apply vertical translation

Using the Vertical Translation and Function Transformations knowledge points
\[
f(x) = \sqrt[5]{x + 8} - 3
\]
</reasoning>

<answer>

Question 15

<mcq-option>A) \(f(x) = 2x + 2\)</mcq-option>
<mcq-option>B) \(f(x) = 0.5x + 2\)</mcq-option>
<mcq-option>C) \(f(x) = 0.5x\)</mcq-option>
<mcq-correct>D) \(f(x) = 2x\)</mcq-correct>

Question 16

<mcq-correct>A) \(f(x) = \sqrt[5]{x + 8} - 3\)</mcq-correct>
<mcq-option>B) \(f(x) = \sqrt[5]{x - 8} - 3\)</mcq-option>
<mcq-option>C) \(f(x) = \sqrt[5]{x + 3} - 8\)</mcq-option>
<mcq-option>D) \(f(x) = \sqrt[5]{x - 3} + 8\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Find the slope of the linear function

Using the Linear Modeling knowledge point
\[
m = \frac{f(2) - f(1)}{2 - 1} = \frac{4 - 2}{1} = 2
\]

Determine the linear equation

Using the Linear Modeling knowledge point
\[

$$\begin{aligned} &f(x) - 2 = 2(x - 1) \\ &f(x) = 2x \end{aligned}$$

\]

Apply horizontal translation

Using the Function Transformations knowledge point
\[
x \to x - (-8) = x + 8
\]

Apply vertical translation

Using the Vertical Translation and Function Transformations knowledge points
\[
f(x) = \sqrt[5]{x + 8} - 3
\]
</reasoning>

<answer>

Question 15

<mcq-option>A) \(f(x) = 2x + 2\)</mcq-option>
<mcq-option>B) \(f(x) = 0.5x + 2\)</mcq-option>
<mcq-option>C) \(f(x) = 0.5x\)</mcq-option>
<mcq-correct>D) \(f(x) = 2x\)</mcq-correct>

Question 16

<mcq-correct>A) \(f(x) = \sqrt[5]{x + 8} - 3\)</mcq-correct>
<mcq-option>B) \(f(x) = \sqrt[5]{x - 8} - 3\)</mcq-option>
<mcq-option>C) \(f(x) = \sqrt[5]{x + 3} - 8\)</mcq-option>
<mcq-option>D) \(f(x) = \sqrt[5]{x - 3} + 8\)</mcq-option>
</answer>

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