Question
Given the function \( f(t)=(t-7)(t+4)(t-1) \) its \( f \)-intercept is its \( t \)-intercepts are
Ask by Campbell French. in the United States
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The \( f \)-intercept is 28, and the \( t \)-intercepts are at \( t = 7 \), \( t = -4 \), and \( t = 1 \).
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
Like
The Deep Dive
To find the \( f \)-intercept of the function \( f(t) = (t-7)(t+4)(t-1) \), we set \( t = 0 \). This gives us \( f(0) = (0-7)(0+4)(0-1) = (-7)(4)(-1) = 28 \). Therefore, the \( f \)-intercept is \( 28 \). For the \( t \)-intercepts, we set \( f(t) = 0 \). This occurs when any factor is zero: \( t-7 = 0 \) leads to \( t = 7 \), \( t+4 = 0 \) leads to \( t = -4 \), and \( t-1 = 0 \) leads to \( t = 1 \). The \( t \)-intercepts are \( t = 7, -4, 1 \).