Question

match each equation with a description of the function it represents.
a. $f(x) = 2x+4$

b. $g(x) = 2(x+4)$

c. $h(x) = 4x+2$

d. $k(x) = 4(x+2)$

1. to get the output, add 4 to the input, then multiply the result by 2.

1. to get the output, add 2 to the input, then multiply the result by 4.

Explanation:

To solve this, we analyze each function and match it to the description:

For Description 1: "To get the output, add 4 to the input, then multiply the result by 2."

Let the input be \( x \). First, add 4 to \( x \): \( x + 4 \). Then multiply by 2: \( 2(x + 4) \). This matches function \( g(x) = 2(x + 4) \) (Option B).

For Description 2: "To get the output, add 2 to the input, then multiply the result by 4."

Let the input be \( x \). First, add 2 to \( x \): \( x + 2 \). Then multiply by 4: \( 4(x + 2) \). This matches function \( k(x) = 4(x + 2) \) (Option D).

For the remaining functions (A and C), we can analyze their operations:

• \( f(x) = 2x + 4 \): Multiply input by 2, then add 4.
• \( h(x) = 4x + 2 \): Multiply input by 4, then add 2.

Assuming there are more descriptions (not fully shown), but based on the given descriptions:

1. Matches B. \( g(x) = 2(x + 4) \)
2. Matches D. \( k(x) = 4(x + 2) \)

If we consider the initial functions and the two given descriptions:

• For "add 4 to input, multiply by 2": The function is \( 2(x + 4) \), which is \( g(x) \) (Option B).
• For "add 2 to input, multiply by 4": The function is \( 4(x + 2) \), which is \( k(x) \) (Option D).

Answer:

1. B. \( g(x) = 2(x + 4) \)
2. D. \( k(x) = 4(x + 2) \)