Question

Given a polynomial function f(x), describe the effects on the y-intercept, regions where the graph is increasing and decreasing, and the end behavior when the following changes are made. Make sure to account for even and odd functions.


When f(x) becomes f(x) − 1
When f(x) becomes −f(x) + 1

Answer 1

The first case is fairly easy that is a shift down by one. Given that you should be able to answer the questions. The second is much trickier that would be a shift down by one and then a vertical flip

Answer 2

So on the first one, everything just goes down one?

Answer 3

for a downward translation of 1, the y-intercept will decrease by 1. This applies to both even and odd functions

Answer 4

For -f(x) +1:

Even functions:
A negation of f(x) will imply the graph is inverted about the x-axis. Which is to say, if the y-intercept of f(x) is given by a, then the y-intercept of -f(x) is given by -a. -f(x)+1 will have a y-intercept of -a+1

Answer 5

oh okay, i think i get it now

Answer 6

could i get help with 1 more?

Answer 7

ok sure, what is it?

Answer 8

Christi is doing her math homework. To receive full credit, she must answer this question:

What key features are necessary—and how are the features used—to create the sketch of a polynomial function?

What is Christi's correct answer, so she receives full credit for the question? Explain in complete sentences.

Answer 9

I would use the info they gave you:

***describe the effects on the y-intercept, regions where the graph is increasing and decreasing, and the end behavior when the following changes are made. Make sure to account for even and odd functions. ***

those sound like the key features.

Answer 10

Oh okay