Question

Dilate each given function to create a new function of a higher degree sketch the graph and then identify the zeros of each new function

Please provide the zeros so I’m able to make the graph pls and thank you <3

Answer 1

Answer:Down Below

Explanation:

1. f(x) = (x-1)(x+1)

To dilate this function, we need to multiply it by a constant. Let's choose 2 as the constant:

g(x) = 2(x-1)(x+1)

Now let's sketch the graph of g(x) and identify the zeros:

The graph of g(x) will be similar to f(x), but stretched vertically. The zeros of g(x) will be the same as the zeros of f(x), which are x = -1 and x = 1.

2. h(x) = (x-1)(x+4)

To dilate this function, we'll multiply it by a constant. Let's choose 3 as the constant:

k(x) = 3(x-1)(x+4)

Sketching the graph of k(x) and identifying the zeros:

The graph of k(x) will be similar to h(x), but stretched vertically. The zeros of k(x) will be the same as the zeros of h(x), which are x = -4 and x = 1.

3. g(x) = (2x + 1)(x - 2)

To dilate this function, we'll multiply it by a constant. Let's choose 4 as the constant:

m(x) = 4(2x + 1)(x - 2)

Sketching the graph of m(x) and identifying the zeros:

The graph of m(x) will be similar to g(x), but stretched vertically. The zeros of m(x) will be the same as the zeros of g(x), which are x = -1/2 and x = 2.

4. j(x) = (x-4)(x + 4)

To dilate this function, we'll multiply it by a constant. Let's choose 5 as the constant:

n(x) = 5(x-4)(x + 4)

Sketching the graph of n(x) and identifying the zeros:

The graph of n(x) will be similar to j(x), but stretched vertically. The zeros of n(x) will be the same as the zeros of j(x), which are x = -4 and x = 4.