Question

need help with this question giving medal

Answer 1

When solving a radical equation, Beth and Kelly came to two different conclusions. Beth found a solution, while Kelly's solution did not work in the equation.

Create and justify two situations: one situation where Beth is correct and a separate situation where Kelly is correct.

Answer 2

@phi @whpalmer4

Answer 3

If you have an equation with a square root on one side, but not the other, and you have to square both sides to solve the equation, you will often introduce what is called an extraneous solution, which is one that solves the new equation (after squaring) but does not work in the original.

This video covers it pretty well, I think: https://www.khanacademy.org/math/algebra/exponent-equations/radical_equations/v/extraneous-solutions-to-radical-equations

Answer 4

also @whpalmer4 could you help with this as well

Answer 5

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) − 3
When f(x) becomes −2 • f(x)

Answer 6

You can reason these out, and should.

You have a function \(f(x)\). Think of it as a little machine that takes a number in (number is represented by \(x\) here), and spits out a number, a unique value for each value of \(x\). Every time you put in a certain value for \(x\), you always get the same number out.

You make a little graphing machine which feeds in all sorts of numbers for \(x\), asks the function machine to do its work, and uses the result as \(y\), then puts a dot at that point \((x,y)\). As it does more and more points, you see the shape appear on the plot.

With me so far?

Answer 7

yes

Answer 8

Okay. What happens if our machine is a little bit out of adjustment, and each time it plots a point, it plots it at a y value which is 3 less than what came out of the function machine?

Answer 9

Does the result have the same shape?

Answer 10

no

Answer 11

?

Answer 12

right

Answer 13

Uh isn't it going to be the same shape, just shifted by 3 units?

Answer 14

oh yeah it is

Answer 15

Suppose the function is the very simple \(y = f(x) = x\): that's just a straight line with slope 1 passing through the origin and going upward and to the right, up 1 step for each step to the right.

If you plot the same thing, but subtract 3 from \(y\) each time, you get a straight line running parallel to the first one, but 3 units lower. It crosses the y axis at (0,-3) instead of (0,0).

Answer 16

oh ok i see it now

Answer 17

Here's another example:

Answer 18

Here are the questions:
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.

What is the effect on the y-intercept?

Do we change the regions where the graph is increasing or decreasing?

Does the end behavior change?

Answer 19

I have to leave now, so you'll need to work this out by yourself, but I'm confident that you can do so. I'll check back in a few hours.