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Find the
y-coordinate of the
y-intercept of the polynomial function defined below.

f(x)=-(x-4)(4x-2)(x-2)^(3)
Answer:

Find the $y$ -coordinate of the $y$ -intercept of the polynomial function defined below. $\newline$ $f(x)=-(x-4)(4 x-2)(x-2)^{3}$ $\newline$ Answer:

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Domain and range of square root functions: equations

Full solution

Q. Find the

y

-coordinate of the

y

-intercept of the polynomial function defined below.

\newline

f(x)=-(x-4)(4 x-2)(x-2)^{3}

\newline

Answer:

Evaluate $f(x)$ at $x=0$ : To find the y-coordinate of the y-intercept of the function $f(x)$ , we need to evaluate $f(x)$ when $x = 0$ . This is because the y-intercept occurs where the graph of the function crosses the y-axis, and the x-coordinate is always $0$ at the y-axis.
Substitute $x=0$ into $f(x)$ : Substitute $x = 0$ into the function $f(x) = -(x-4)(4x-2)(x-2)^{3}$ . $\newline$ $f(0) = -(0-4)(4\cdot 0-2)(0-2)^{3}$
Simplify the expression: Simplify the expression by performing the operations. $\newline$ $f(0) = -(-4)(-2)(-2)^{3}$ $\newline$ $f(0) = -(-4)(-2)(-8)$
Continue simplifying: Continue simplifying the expression. $\newline$ $f(0) = -(-4)\times 2\times 8$ $\newline$ $f(0) = -(-32)\times 8$ $\newline$ $f(0) = 256$
Find y-coordinate of y-intercept: The y-coordinate of the y-intercept is the value of $f(0)$ , which we have found to be $256$ .

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