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In $4-7,$ the graph of $y=f(x)$ is shown. a. Find $f(0)$ for each function. b. Find $x$ when $f(x)=0 .$ Foreach function, there may be no values, one value, or more than one value. c. Sketch the graph of$y=f(x)+2 .$ d. Sketch the graph of $y=2 f(x) .$ e. Sketch the graph of $y=-f(x) .$

a) $f(0)=1$b) $x=1$c-e) See graph

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 6

The Algebra of Functions

An Introduction to Geometry

Functions

Linear Functions

Polynomials

Missouri State University

Oregon State University

McMaster University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

02:42

In $4-7,$ the graph of $y=…

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Each figure shows the grap…

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each figure shows the grap…

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02:24

$5-14$ . Suppose the graph…

01:14

Sketch the graph of each f…

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01:49

(A) Graph $f(x)=2^{x}-4$

02:13

All right. So for this problem, we are given the graph of a function, and the first thing we have to do is find what f zero is. So I'm just gonna write the equation for this graph. This equation is y equals negative X plus one. So what we need to do is find out what f zero is. So if we plug in zero, we get negative. Zero plus one equals one. So f of zero is equal to one. For the second part of the problem, we need to find the value that makes the output equal to zero. So in this case that we just look at our graph, we see that Y is equal to zero when x is equal and negative one. So for f of x two, equal zero X must equal negative one. Okay. Uh, I'm sorry. Not negative. One positive. Positively. Okay. And now we need to scratch the graph of y equals F of X plus two. So literally. All we have to do is just added two right here, and our new equation becomes y equals negative X plus three. So we're just gonna move up to here Craft a few points and draw that in. Okay, All right. And the next thing we have to do is sketch the graph of two f of X. So if we multiply, y equals negative X plus one by two, we get y equals negative to X plus two. So we go to here, too. On our slope is negative, too. So this graph looks a little something like that. Okay. And for our last problem or less portion of the problem, we need to sketch the graph of negative F of X. So if we were to multiply this entire equation very negative one, we would get y equals X minus one. So now we have minus one is they're intercepting. We have positive slope. So that graph looks like this, okay?

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