I desperately need assistance with my math homework very quickly please!

Question

1.) Identify the intercepts of f(x) and g(x).

A.) f(x) x-intercepts: −5 and 5

f(x) y-intercept: −25

g(x) x-intercepts: −5 and 5

g(x) y-intercept: −5

B.) f(x) x-intercepts: −5 and 5

f(x) y-intercept: −25

g(x) x-intercepts: −5 and 5

g(x) y-intercept: −25

C.) f(x) x-intercepts: −5 and 5

f(x) y-intercept: 25

g(x) x-intercepts: −1 and 1

g(x) y-intercept: −5

D.) f(x) x-intercepts: −5 and 5

f(x) y-intercept: −25

g(x) x-intercepts: −1 and 1

g(x) y-intercept: −25

2.) Which function should be used to when evaluating the function at x = −5?

A.) 

B.) 

please please explain and solve

Answer 1

1.) Identify the intercepts of f(x) and g(x).

f(x) = x² - 25

x² - 5²

(x + 5) (x -5)

x-intercept, roots:

x₁ = -5

x₂ = 5

y-intercept:

f₍₀₎ = 0² - 25

f₍₀₎ = -25

y-intercept: -25

g_(x) = 1/5 f(x)

g_(x) = 1/5 (x² - 25)

Function f(x) is vertically compressed by 1/5, so it has the same roots:

x-intercept, roots:

x₁ = -5

x₂ = 5

y-intercept:

g₍₀₎ = 1/5 (0 - 25)

g₍₀₎ = 1/5 (-25)

g₍₀₎ = -5

y-intercept: -5

Option A:

A.) f(x) x-intercepts: −5 and 5

f(x) y-intercept: −25

g(x) x-intercepts: −5 and 5

g(x) y-intercept: −5

2.) Which function should be used to when evaluating the function at x = −5?

x = -5

-5 ≤ 3

Then, you should use option B:

B.)