Which description is correct for the x-intercept(s) of Function A and Function B?
Function A:
x g(x)
−2 0
3 7
5 0
−1 2
0 −2
Function B: f(x)=|x|−3
A.Both functions have one negative and one positive x-intercept.
B. Function B has two x-intercepts.
Function A has one x intercept.
C. Function A has two x-intercepts.
Function B has one x-intercept.
D. Both functions have the same x-intercept(s).
To determine the x-intercepts of a function, we need to find the values of x where the function intersects or crosses the x-axis. This occurs when the y-coordinate (the value of the function) is equal to 0.
For Function A, we can see that its x-intercepts occur when g(x) = 0. Looking at the table, the x-values for which g(x) = 0 are -2 and 5. Therefore, Function A has two x-intercepts.
For Function B, the equation is f(x) = |x| - 3. To find the x-intercept, we set f(x) = 0 and solve for x: |x| - 3 = 0. Adding 3 to both sides gives |x| = 3. Since the absolute value of a number is non-negative, this equation can be rewritten as x = 3 or x = -3. So, Function B has two x-intercepts as well.
The correct description for the x-intercepts of Function A and Function B is:
C. Function A has two x-intercepts.
Function B has one x-intercept.