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Given the following graph,

$\cdot$ Evaluate $f(0)$

$\cdot$ Solve for $f(x)=-3$

$\mathrm{f}(0)=1$

$f(2)=-3$ and $f(-2)=-3$

in other words $x=2$ or $x=-2$

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Numerade Educator

Missouri State University

Harvey Mudd College

Numerade Educator

Okay, so we begin this problem with a graph. Here are some of the features we see on the graph. It has a basic kind of w type shape. Gonna come down like this is gonna go up. It's gonna wrap around. It's gonna come back around, back up some of the points that we can see on the graph. Quite clearly, we have a 01 That is a point on the graph. We have a point down here. This point is at negative 23 All right. And then we have this point over here. This point is that positive? To negative three. We went right to down three. This should be negative here. Okay, so we've got those basic points. Crap is going up on both ends, and we are asked for this function. The graph is half of acts. Remember, the f of X g of x n of x p of x is why, and we're asking this question to find the value of find the value of f of zero. Okay, So as we said since the general idea is that f of axe and of Xbox is why what we're saying here is if x zero What is why on this craft? And if you look here this point if x zero, if I don't go left to right, what do I do with up? Down I go up one to be on the graph. So the answer to FF zero is one. Why is one when x zero on this raft? You separately from that we are asked to solve so half of the f of X is equal to negative three. Okay, remember again half of axe is why So we're saying we want why to be negative three. We want to know what are the values of X that make y equal date of negative three y equals negative. Three would be a horizontal line down here. So we draw the line y equals negative three. And we ask ourselves, where are the points on the graph that touched this line? We've got one right here. We've got another one right here. If you think about X y right, once Roy's like X y were saying If why is negative 31 sex and we can see in one case too. In another case. Negative too. So in solving this equation. The values of X, for which F of X is equal. Negative. Three. We would say X is equal to two are negative too. Or we could contents and say as plus minus two. Okay, we are.

Hartwick College