Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

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].

Sagot :

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]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.