Question

In two or more complete sentences compare the number of x-intercepts of the graph of f(x)=x^2 to the number of x-intercepts of the graph of g(x)=x^2-7 be sure to include the transformations that occurred between the parent function f(x) and its image

Answer 1

In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x^2 to the number of x-intercepts in the graph of g(x) = -x^2 +7. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).

When the function is moved upward 7 units(+7) and the sign is changed to -x^2, it is concave upward, rather than downward, and now it will have two x-intercepts or roots, at (sqrt(7),0) and (-sqrt(7),0)

graph%28300%2C300%2C-5%2C5%2C-5%2C10%2Cx%5E2%2C-x%5E2%2B7%29 the answer is 4

Explanation:

Answer 2

The function g(x) has a greater number of x-intercepts that the function f(x)

The parent function f(x) = x² is shifted down by 7 units to get g(x) = x² - 7

How to compare the number of x-intercepts of the graphs

From the question, we have the following parameters that can be used in our computation:

f(x) = x²

g(x) = x² - 7

From the above, we have that

g(x) = f(x) - 7

This means that

The parent function f(x) = x² is shifted down by 7 units to get g(x) = x² - 7

Setting the functions to 0, we have

f(x) = x² = 0

x = 0 i.e. one x-intercept

g(x) = x² - 7 = 0

x² = 7

x = ±√7 i.e. two x-intercepts

Hence, the function g(x) has a greater number of x-intercepts that the function f(x)