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

Question

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: (−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 negative 2 right parenthesis ; Function 2: left parenthesis 0 comma 2 right parenthesis . Function 2 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.

Answer 1

To find the y-intercept of Function 1, \( f(x) = 4x + 2 \), we set \( x = 0 \):

\[ f(0) = 4(0) + 2 = 2 \]

Thus, the y-intercept of Function 1 is \( (0, 2) \).

For Function 2, which is described as a diagonal line connecting two data points, without loss of generality, let's assume the data points given are \( (0, -2) \) and \( (0, 2) \). The y-intercept could be either of these values depending on the exact endpoints of the diagonal line.

Now, we're comparing:

• Function 1: \( (0, 2) \)
• Function 2: \( (0, -2) \) (assuming this is one of the data points)

In this case, the y-values are:

• Function 1: 2
• Function 2: -2

Clearly, \( -2 \) (from Function 2) is smaller than \( 2 \) (from Function 1).

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