Hello please please help with my homework asap

Question

1.) Determine whether f is an exponential function of x. If so, find the constant ratio.

A.) f is not an exponential function.

B.) f is an exponential function with a constant ratio of 1/2.

C.) f is an exponential function with a constant ratio of 2.

D.) f is an exponential with a constant difference of 2.

2.) What change do you have to make to the graph of f (x) = 11x in order to graph the function g (x) = 11x + 12?

Shift the graph _____ units _____.

A.) 11, up

B.) 12, down

C.) None of these

D.) 12, up

E.) 11, down

Answer 1

If it is an exponential function it has the form f(x) = c.a^x

Now let us substitute using the values of the table.

f(-1) = c.a^-1 = c/a= 1/4

f(0) = c.a⁰ = c = 1/2

Since any number raised to the zero we can use this to find the value of a.

Remember f(-1) = c.a^-1 = 1/4

Multiply both sides by a and get

1/2 = c = a/4 so a = 4(1/2) =2

You can check to see it works for the other values in the table.

Another way to approach this is to note that the values of f(x) each time x increases by 1.

For the second question, note that shifting a function up wards by a units increases f(x) by a so it is a units higher than the original.

Answer 2

Hi Austin! I believe the answers are C and D -- I hope that helps :-)