To determine the [tex]$x$[/tex]-intercepts of the function [tex]$f(x) = x^2 - 25$[/tex], we need to find the values of [tex]$x$[/tex] where [tex]$f(x) = 0$[/tex]. This involves solving the equation:
[tex]\[ f(x) = 0 \][/tex]
Given our function:
[tex]\[ x^2 - 25 = 0 \][/tex]
To solve for [tex]$x$[/tex], we first isolate the [tex]$x^2$[/tex] term:
[tex]\[ x^2 = 25 \][/tex]
Next, we take the square root of both sides of the equation to solve for [tex]$x$[/tex]:
[tex]\[ x = \pm \sqrt{25} \][/tex]
This simplifies to:
[tex]\[ x = \pm 5 \][/tex]
Therefore, the [tex]$x$[/tex]-intercepts of the function are [tex]$x = 5$[/tex] and [tex]$x = -5$[/tex].
Given the options:
A. -15
B. -20
C. -5
D. -25
We can see that the only [tex]$x$[/tex]-intercept from the given options is:
C. -5
Thus, the correct answer is C. -5.
