Question

The graph of f(x) = 2x + 3 shifts 10 units to the right when it is replaced with the graph of f(x) = 2x − k. What is the value of k?

A: 3
B: 7
C: 10
D: 13

Answer 1

B: 7

Explanation:

If you think about it, we have the function f(x), right? Now just imagine a marker on the 3, because we know the function is there, hence the 3 added to the exponent of x. But the equation f(x) = 2^(x-k) took away the 3. so with the function down to 0 instead of 3, how far do we have to go down to get to 10 below the 3 marker? If we move 10 units below the 3 mark, we are at -7 on the y line, right?

So, now we know the ending y value is going to be -7, so how much do we need to subtract from 0 to get there? 7!

Here's a drawing if it helps simplify it:

Note: sorry if the number line is confusing! it's only purpose is to show the value of x, sorry if that does seem very clear! My bad -v-'

Answer 2

B. Every time you shift a graph one unit to the right, your “k” value will subtract by one. Therefore, 3 - 10 = -7