Given the function h(x)=x^2-6x+2 evaluate each of the following. evaluate h(-2x)

Answer 1

Sometimes students are confused by the fact that the function definition contains the letter x and then they are asked to evaluate the function at an expression that also contains the letter x.

Try visualizing the function definition with empty parentheses, like this:

h() = ()² - 6() + 2.

The input to the function goes wherever there are empty parentheses.

So to find h(-2x):

h(-2x) = (-2x)² - 6(-2x) + 2

= 4x² +12x + 2

Suppose you are asked to find h(x + k).

h(x + k) = (x+k)² - 6(x + k) + 2

= x² +2kx + k² - 6x -6k + 2

And of course the input can be a number:

h(3) = (3)² - 6(3) + 2

= 9 - 18 +2

= -7