What are the y-values for these x-values?

Question

For each of the following, sketch a graph of the new function and use your graph to fill in the y-values in the tables. Assume that the function f(x) is only defined on −5≤x≤5; for any undetermined values in the new functions, enter dne.

Transformation: y=3−f(x)

What are the y-values for these x-values: -4, -2, 0, 2, 4

Answer 1

For this problem, we find the y-value (the vertical position of the blue line in the graph) at a given x-value (the horizontal position of the blue line in the graph) and plug that value into the equation for "f(x)". We do that for each of the five given x-values.

x=-4:

On the graph, at x=-4, we look vertically above and find the blue line at a value of 2. Plugging 2 into the equation, gives:

y=3-2=1

The same can be done for the other x-values:

x=-2 --> f(x) = 2 --> y = 3-2=1

x=0 --> f(x) = -4 --> y=3-(-4)=3+4=7

x=2 --> f(x)=-10 --> y=3-(-10)=3+10=13

x=4 --> f(x)=-11 --> y=3-(-11)=3+11=14