Question

Suppose f(x)=−7x^8+30x^6−17.
(a) Then f(−x)=? (Simplify)

Transformations and shifts help

Answer 1

x is raised to an even power in each case
so f(x)=f(-x), it is an even function

Answer 2

which means?

Answer 3

reflected over the y axis

Answer 4

not reflected, means it is symmetric with respect to y-axis

Answer 5

so how do we simplify that problem

Answer 6

simplify it?

Answer 7

oh, you want the transformation....yes f(-x) is the graph of f(x) reflected across the y-axis, but the graph will look exactly the same considering that f(x) is already symmetric with respect to y-axis

Answer 8

so what will my new equation be?

Answer 9

is it just the same thing?

Answer 10

f(x)=−7x^8+30x^6−17
f(-x)=-7(-x)^8+30(-x)^6-17
simplified means remove the negative sign where it isn't required.
since (-x) raised to any even power is positive, you can remove both negatives
f(-x)=-7x^8+30x^6-17

Answer 11

bingo!

Answer 12

−8x7+12x−12
f(-x) = ?

would this be the same thing then?

Answer 13

−8x7^+12x−12

Answer 14

got it. Now i have a problem with this Write a formula (in terms of the independent variable w) for the transformation of k(w)=5^w given below. y=−k(w−3)= ???