Questions: Polynomial and Rational Functions Finding x-and y-intercepts given a polynomial function Find all x-intercepts and y-intercepts of the graph of the function. f(x)=x^3-4x^2-4x+16 x-intercept(s): None y-intercept(s): 16

Polynomial and Rational Functions
Finding x-and y-intercepts given a polynomial function

Find all x-intercepts and y-intercepts of the graph of the function.
f(x)=x^3-4x^2-4x+16

x-intercept(s):
None

y-intercept(s):
16

Transcript text: Polynomial and Rational Functions Finding $x$-and $y$-intercepts given a polynomial function Find all $x$-intercepts and $y$-intercepts of the graph of the function. \[ f(x)=x^{3}-4 x^{2}-4 x+16 \] $x$-intercept(s): None $y$-intercept(s): 16

Solution

Solution Steps

To find the $x$-intercepts of the polynomial function $ f(x) = x^3 - 4x^2 - 4x + 16 $, we need to solve the equation $ f(x) = 0 $. This involves finding the roots of the polynomial. For the $y$-intercept, we evaluate the function at $ x = 0 $.

Step 1: Finding the $ x $-intercepts

To find the $ x $-intercepts of the function $ f(x) = x^3 - 4x^2 - 4x + 16 $, we solve the equation $ f(x) = 0 $. The roots of the polynomial are found to be: \[ x = -2, \quad x = 2, \quad x = 4 \]

Step 2: Finding the $ y $-intercept

The $ y $-intercept is found by evaluating the function at $ x = 0 $: \[ f(0) = 16 \]