ashleenbond
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Select the correct answer.

What are the [tex]$x$[/tex]-intercept and the [tex]$y$[/tex]-intercept of this function?

[tex]\[ f(x)=4x+12 \][/tex]

A. The [tex]$x$[/tex]-intercept is [tex]$ (3,0) $[/tex], and the [tex]$y$[/tex]-intercept is [tex]$ (0,-12) $[/tex].

B. The [tex]$x$[/tex]-intercept is [tex]$ (-3,0) $[/tex], and the [tex]$y$[/tex]-intercept is [tex]$ (0,-12) $[/tex].

C. The [tex]$x$[/tex]-intercept is [tex]$ (3,0) $[/tex], and the [tex]$y$[/tex]-intercept is [tex]$ (0,12) $[/tex].

D. The [tex]$x$[/tex]-intercept is [tex]$ (-3,0) $[/tex], and the [tex]$y$[/tex]-intercept is [tex]$ (0,12) $[/tex].



Answer :

GinnyAnswer
To find the [tex]\( x \)[/tex]-intercept and [tex]\( y \)[/tex]-intercept of the function [tex]\( f(x) = 4x + 12 \)[/tex], let's go through the steps in detail.

### Finding the [tex]\( x \)[/tex]-Intercept
The [tex]\( x \)[/tex]-intercept is the point where the graph of the function crosses the [tex]\( x \)[/tex]-axis. This occurs when [tex]\( f(x) = 0 \)[/tex].

1. Set [tex]\( f(x) = 0 \)[/tex]:
[tex]\[ 0 = 4x + 12 \][/tex]
2. Solve for [tex]\( x \)[/tex]:
[tex]\[ 4x + 12 = 0 \][/tex]
[tex]\[ 4x = -12 \][/tex]
[tex]\[ x = \frac{-12}{4} \][/tex]
[tex]\[ x = -3 \][/tex]
So, the [tex]\( x \)[/tex]-intercept is at the point [tex]\((-3, 0)\)[/tex].

### Finding the [tex]\( y \)[/tex]-Intercept
The [tex]\( y \)[/tex]-intercept is the point where the graph of the function crosses the [tex]\( y \)[/tex]-axis. This occurs when [tex]\( x = 0 \)[/tex].

1. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 0 \)[/tex]:
[tex]\[ f(0) = 4 \cdot 0 + 12 \][/tex]
2. Calculate the value:
[tex]\[ f(0) = 12 \][/tex]
So, the [tex]\( y \)[/tex]-intercept is at the point [tex]\((0, 12)\)[/tex].

Based on this detailed solution, the correct answer is:
D. The [tex]\( x \)[/tex]-intercept is [tex]\((-3,0)\)[/tex], and the [tex]\( y \)[/tex]-intercept is [tex]\((0, 12)\)[/tex].

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