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:

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

$$
LATEXBLOCK0
$$

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

$$ f(x) = \sqrt[5]{x + 8} - 3 $$

Answer:

Question 15

• A) \(f(x) = 2x + 2\)
• B) \(f(x) = 0.5x + 2\)
• C) \(f(x) = 0.5x\)
• D) \(f(x) = 2x\) (Correct answer)

Question 16

• A) \(f(x) = \sqrt[5]{x + 8} - 3\) (Correct answer)
• B) \(f(x) = \sqrt[5]{x - 8} - 3\)
• C) \(f(x) = \sqrt[5]{x + 3} - 8\)
• D) \(f(x) = \sqrt[5]{x - 3} + 8\)