Question Describe the transformation(s) of polynomial $p(x) = -3(x-2)(x-4)(x+1)$ when transformed to $-p(x)$ .

Studdy Solution

STEP 1

Assumptions
1. The original polynomial function is $p(x) = -3(x-2)(x-4)(x+1)$ .
2. We are considering the transformation of $p(x)$ to $-p(x)$ .

STEP 2

Understand the effect of the transformation $-p(x)$ on the original polynomial $p(x)$ .
The transformation $-p(x)$ will multiply the original polynomial by $-1$ .

STEP 3

Apply the transformation to the polynomial function.
$-p(x) = -(-3(x-2)(x-4)(x+1))$

STEP 4

Simplify the expression by distributing the negative sign.
$-p(x) = 3(x-2)(x-4)(x+1)$

STEP 5

Describe the transformation that has occurred.
The transformation from $p(x)$ to $-p(x)$ reflects the graph of the polynomial across the x-axis. This is because multiplying the function by $-1$ changes the sign of all the y-values of the original function, effectively flipping the graph over the x-axis.
The solution to part a) is that the transformation of $p(x)$ to $-p(x)$ reflects the graph of the polynomial across the x-axis.

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