Questions: Question 1 Given the function f(x)=(x-1)(x+4)(x-7) : the coordinates of its f-intercept are the coordinates of its x-intercepts are

Transcript text: Question 1 Given the function $f(x)=(x-1)(x+4)(x-7)$ : the coordinates of its $f$-intercept are $\square$ the coordinates of its $x$-intercepts are $\square$ Question Help: Video Message instructor Submit Question

Solution

Solution Steps

Solution Approach

To find the $f$-intercept (y-intercept), we need to evaluate the function $f(x)$ at $x=0$.
To find the $x$-intercepts, we need to solve the equation $f(x) = 0$.

Step 1: Finding the $ f $-intercept

To find the $ f $-intercept, we evaluate the function at $ x = 0 $: \[ f(0) = (0 - 1)(0 + 4)(0 - 7) = (-1)(4)(-7) = 28 \] Thus, the coordinates of the $ f $-intercept are $ (0, 28) $.

Step 2: Finding the $ x $-intercepts

To find the $ x $-intercepts, we solve the equation $ f(x) = 0 $: \[ (x - 1)(x + 4)(x - 7) = 0 \] This gives us the solutions: \[ x - 1 = 0 \quad \Rightarrow \quad x = 1 \] \[ x + 4 = 0 \quad \Rightarrow \quad x = -4 \] \[ x - 7 = 0 \quad \Rightarrow \quad x = 7 \] Thus, the coordinates of the $ x $-intercepts are $ (-4, 0) $, $ (1, 0) $, and $ (7, 0) $.