Asked by Desiree LeBoeuf on Apr 24, 2024
Verified
Find the x- and y- intercepts, if any, of y=∣x∣−2y = | x | - 2y=∣x∣−2 .
A) x- intercept at 0 , y- intercept at -2
B) x- intercept at ±2\pm 2±2 , y- intercept at 2
C) x- intercept at -2 , y- intercept at -2
D) x- intercept at ±2\pm 2±2 , y- intercept at -2
E) no intercepts
X-intercepts
The points at which a graph intersects the x-axis, indicating the values of x when the function's output equals zero.
Y-intercepts
The points where a graph intersects the y-axis of a coordinate plane.
- Investigate the connections related to points and lines, emphasizing their linear alignment and intercept positions.
Verified Answer
JK
Jazmin Kaleiohi7 days ago
Final Answer :
D
Explanation :
To find the x-intercept, we need to set y to 0 and solve for x:
0=∣x∣−2∣x∣=2x=±2\begin{align*}0&=|x|-2\\|x|&=2\\x&=\pm2\end{align*}0∣x∣x=∣x∣−2=2=±2
Therefore, there are x-intercepts at -2 and 2.
To find the y-intercept, we need to set x to 0 and solve for y:
y=∣0∣−2=−2\begin{align*}y&=|0|-2=-2\end{align*}y=∣0∣−2=−2
Therefore, there is a y-intercept at -2. Choice (D) shows these points correctly.
0=∣x∣−2∣x∣=2x=±2\begin{align*}0&=|x|-2\\|x|&=2\\x&=\pm2\end{align*}0∣x∣x=∣x∣−2=2=±2
Therefore, there are x-intercepts at -2 and 2.
To find the y-intercept, we need to set x to 0 and solve for y:
y=∣0∣−2=−2\begin{align*}y&=|0|-2=-2\end{align*}y=∣0∣−2=−2
Therefore, there is a y-intercept at -2. Choice (D) shows these points correctly.
Learning Objectives
- Investigate the connections related to points and lines, emphasizing their linear alignment and intercept positions.