If f(x) is a third degree polynomial function and g(x) = f(2x) + 2, which of the following must be true? f(x) and g(x) have the same x-intercepts. f(x) and g(x) have the same y-intercepts. f(x) and g(x) have the same number of zeros. f(0) = g(0) – 2

Choice D) which is f(0) = g(0) - 2

Step-by-step explanation:

Plug x = 0 into the g(x) function to find that

g(x) = f(2*x) + 2

g(0) = f(2*0) + 2 replace every x with 0

g(0) = f(0) + 2

g(0) - 2 = f(0) + 2 - 2 subtract 2 from both sides

g(0) - 2 = f(0)

f(0) = g(0) - 2

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation: