Answered

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 determine the [tex]\( x \)[/tex]-intercept and the [tex]\( y \)[/tex]-intercept of the function [tex]\( f(x) = 4x + 12 \)[/tex], we follow these steps:

1. Finding the [tex]\( y \)[/tex]-intercept:

The [tex]\( y \)[/tex]-intercept occurs where the graph of the function crosses the [tex]\( y \)[/tex]-axis. This happens when [tex]\( x = 0 \)[/tex].
- Substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[ f(0) = 4 \cdot 0 + 12 = 12 \][/tex]
So, the [tex]\( y \)[/tex]-intercept is [tex]\((0, 12)\)[/tex].

2. Finding the [tex]\( x \)[/tex]-intercept:

The [tex]\( x \)[/tex]-intercept occurs where the graph of the function crosses the [tex]\( x \)[/tex]-axis. This happens when [tex]\( f(x) = 0 \)[/tex].
- Set the function equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[ 4x + 12 = 0 \][/tex]
- Subtract 12 from both sides:
[tex]\[ 4x = -12 \][/tex]
- Divide both sides by 4:
[tex]\[ x = -3 \][/tex]
So, the [tex]\( x \)[/tex]-intercept is [tex]\((-3, 0)\)[/tex].

Therefore, the [tex]\( x \)[/tex]-intercept is [tex]\((-3, 0)\)[/tex] and the [tex]\( y \)[/tex]-intercept is [tex]\((0, 12)\)[/tex].

Hence, the correct answer is:
[tex]\[ \boxed{\text{D. The } x\text{-intercept is }(-3,0)\text{, and the }y\text{-intercept is }(0,12)\text{.}} \][/tex]