Answer :
Answer:
Depending on what you are looking for, the y-intercept of [tex]f(x)= -|-2x| + 3[/tex] is 3, while the x-intercepts are ± 1.5.
Step-by-step explanation:
f(x) is the equivalent of 'y' in this equation, so doing so yields the new equation [tex]y = -|-2x| + 3[/tex]. The y-intercept of any equation always occurs at [tex]x = 0[/tex], so plugging 0 as x into the equation:
- [tex]y = -|-2(0)| + 3[/tex]
- [tex]y = -|0| + 3[/tex]
- [tex]y = 3[/tex]
As for the x-intercepts, they always occur at [tex]y = 0[/tex], so plugging 0 as y into the equation yields [tex]0 = -|-2x| + 3[/tex], which can be used to solve for x:
- [tex]-|-2x| = -3[/tex]
- [tex]|-2x| = 3[/tex]
- [tex]-2x = 3[/tex] and [tex]-2x = -3[/tex]
- [tex]2x = -3[/tex] and [tex]2x = 3[/tex]
- [tex]x = -1.5[/tex] and [tex]x = 1.5[/tex]
