in-4-7-the-graph-of-yfx-is-shown-a-find-f0-for-each-function-b-find-x-when-fx0-for-each-function-t-2

Question

In $4-7,$ the graph of $y=f(x)$ is shown. a. Find $f(0)$ for each function. b. Find $x$ when $f(x)=0 .$ For
each 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 $y=-f(x) .$

Finian Lickona · Accepted Answer

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&#x27;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&#x27;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&#x27;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&#x27;re intercepting. We have positive slope. So that graph looks like this, okay?

Finian Lickona · Answer

All right, So for this exercise, we are given this graph and that little circle right there means that is an open point. So that&#x27;s not a close point to close point is up here, and the first thing we want to do is find what f zero is. So if we look at our graph, we see that f of zero outputs one so f zero equals one. And for the second part of the question, we have to find where the function takes on the value zero. So as we can see, that never happens, because the zero point right here ah, is not touched by the graph. It&#x27;s a piece wise functions. So, uh, there is no value for which ffx zero, so that would be undefined. For the second part of the graph, we have to sketch a second out of the problem. We have to sketch the graph of F of X plus two. So that&#x27;s literally just going to shift everything up by two. So this line goes up to here, and this line goes up to here, and we&#x27;re gonna have to erase that closed point right there because we actually have an open point right there. It&#x27;s less the graph of if I&#x27;m exposed to thesis and portion are the next portion of the question is to sketch the graph of y equals two f of X and we actually don&#x27;t have to do anything, because if we were to scale these functions, that by a factor of two it would just stretch them in the direction they&#x27;re already going. So the graph of y equals half a to F of X is actually identical to the original graph. And then lastly, we need to sketch the graph of why equals negative too. Next time, no, not may give to just negative f of X. And for this, what&#x27;s going to happen here is himself a trade with race everything. Um dang, it erases my original graph to Okay, I&#x27;m just gonna leave that alone. And so, uh, what is basically gonna happen is our graph is going to flip. So this portion of the graph, which is above the X axis, is now going to be down here, and this is going to actually be a closed point because this line has a close point. And then this portion of the graph is going to move up here and again. It has an open point. Okay,

Ankit Gupta · Answer

in the first part to get the draft off. Why equals two minus half off X The boys, huh? Minus three minus two minus two minus one four. Minus one six minus three. The graph off the following will be like this now in the second part to get the graph off, why equals two F off minus X. The voice are pre to to one minus four one minus six Tree. The graph off the falling will be like this. No. In the third part to get the graph. Oh, why equals to do half off x. The points are minus 34 minus two. Do four. Do six. Fix the graph off. The following will be like this in the fourth park from graph half off. Zero is equal. Do what

James Kiss · Answer

were given a function here and for just the graph of the function. For part a one a graph y equals negative after bags. Well, that negative out front is a reflection vertically over the X axis. So take the points that are highlighted, like negative 32 reflected over the X axis negative to negative one, then 41 with a four negative one 63 will go to 6 93 Got a little curved to that one horizontal piece in a straight line. So that&#x27;s part a. Our bill doing Green R B wants us to graph y equals f of negative eggs. Well, this is a reflection as well, but it&#x27;s over the horizontally over the why access. So I take the point. Negative 32 horizontally would take us to 32 negative 21 would go to negative or positive 21 for one would go to negative for one 63 would go to negative 63 So we&#x27;ve gone are curve heart or his Arnold part and straight part that is part B reflected over the Y axis ever part C I&#x27;m gonna do and red we want to find why or graph y equals two times after vax. Well, that&#x27;s two multiplied outside of function. It&#x27;s a vertical stretch of choose. We take our original points in grass them so that they are twice as tall, vertically, so negative. Three. To put a negative 34 negative to one that&#x27;s a vertical height of one double. It were at negative 22 two Looks me for one on the original would go two for two in 63 would go to 66 Got a horizontal piece are straight line in a bit of a curve and that would be a part C. We also have a part to you, which wants us to find F zero. An included zero on the original function is an output of one.

Ankit Gupta · Answer

in the first bar to get the drop off by is equal to minus half of X. The points are my has 40 minus Do minus three do by enough Latin six minus one. The graph of the fulling will be like this in the second part to get the draft off. Why equals two? Uh huh. Minus X that warrants are four Zito do three minus 21 minus six one. The graph off the following will be like this in the heart of fire for why it was too three f off Eric&#x27;s. The points are minus 40 minus two nine Oh, pre six free. The graph off the fully will be like this In the fourth part, a four is equal to one.

Problem

In $4-7,$ the graph of $y=f(x)$ is shown. a. Find…

Problem 5 Easy Difficulty

In $4-7,$ the graph of $y=f(x)$ is shown. a. Find $f(0)$ for each function. b. Find $x$ when $f(x)=0 .$ For
each 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 $y=-f(x) .$

Answer

a) $f(0)=-2$
b) $x=\pm 2$
c-e) See graph

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a) $f(0)=-2$b) $x=\pm 2$c-e) See graph

Algebra 2 and Trigonometry

Anna Marie V.

Alayna H.

Kayleah T.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Anna Marie V.

Alayna H.

Kayleah T.

Michael J.

a) $f(0)=-2$
b) $x=\pm 2$
c-e) See graph

Ann Xavier Gantert

Algebra 2 and Trigonometry