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Use the image to answer the question.

Function 1: f(x)=4x+2


Function 2:

A diagonal line connects two data points on a coordinate plane.

Compare the two functions and identify the y-values of the y-intercepts. Which function has the smaller value?

(1 point)
Responses

Function 1: (0,−2)
; Function 2: (0,2)
. Function 2 has the smaller value.
Function 1: left parenthesis 0 comma negative 2 right parenthesis ; Function 2: left parenthesis 0 comma 2 right parenthesis . Function 2 has the smaller value.

Function 1: (−2,0)
; Function 2: (2,0)
. Function 1 has the smaller value.
Function 1: left parenthesis negative 2 comma 0 right parenthesis ; Function 2: left parenthesis 2 comma 0 right parenthesis . Function 1 has the smaller value.

Function 1: (0,2)
; Function 2: (0,−2)
. Function 2 has the smaller value.
Function 1: left parenthesis 0 comma 2 right parenthesis ; Function 2: left parenthesis 0 comma negative 2 right parenthesis . Function 2 has the smaller value.

Function 1: (−1,0)
; Function 2: (−1,0)
. They have identical values.
Function 1: left parenthesis negative 1 comma 0 right parenthesis ; Function 2: left parenthesis negative 1 comma 0 right parenthesis . They have identical values.
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1 answer

To find the y-intercepts of the functions, we can calculate them as follows:

  1. Function 1: \( f(x) = 4x + 2 \)

    • To find the y-intercept, we set \( x = 0 \): \[ f(0) = 4(0) + 2 = 2 \] Thus, the y-intercept of Function 1 is \( (0, 2) \).

  2. Function 2: The y-intercept must be derived from the image, as it is a diagonal line connecting two data points. Assuming for our analysis, the y-intercept is the point where the line crosses the y-axis, which has been provided as \( (0, -2) \).

Now that we have the y-intercepts:

  • Function 1: \( (0, 2) \)
  • Function 2: \( (0, -2) \)

Now we compare the y-intercepts:

  • The y-value for Function 1 is 2.
  • The y-value for Function 2 is -2.

Since -2 is less than 2, we can conclude:

Function 2 has the smaller value.

So the correct response is: Function 1: (0, 2); Function 2: (0, -2). Function 2 has the smaller value.