How do you obtain the graph of

Question

How do you obtain the graph of $y=-3f\left(x\right)$ from the graph of $y=f\left(x\right)$ ?

Accepted Answer

Hello there today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. So given the function Y equals G FX, how would the graph of Y equals negative five multiplied by G FX differ from the original graph? Awesome. So it appears for this particular problem we're trying to compare two separate graphs. So we're trying to compare Y equals G FX to Y equals negative five multiplied by G FX. And we're trying to figure out how the second graph which is Y equals negative five multiplied by G FX will differ from the original graph of Y equals G FX. So now that we know ex what exactly we're solving for. Let's take a moment here to read off our multiple choice answers. To see what our final answer might be. A is the graph is reflected across the Y axis and stretched vertically by a factor of five B is the graph is reflected across the X axis and is stretched vertically by a factor of five C is the graph is shifted five units to the right and D is the graph is reflected across the X axis and stretched horizontally by a factor of five. Awesome. So this problem is gonna be really easy to solve for in four easy steps. So first off, let us break it down in the steps. So we have steps one, two, three and four. So we have four simple steps that we're gonna follow to solve for this particular problem. So once again, we need to identify the original function, which the original function we're told is Y equals G FX. That is our original function. So our first step, let's call this I for identify. So we've identified the original function as Y equals G FX. And this function will represent the base graph to which all of our transformations will be applied. Our second step is we need to understand, in order to denote this, as you, we need to understand that the transformation applied to the graph of Y equals G FX in order to obtain Y equals negative five, multiplied by G FX will involve a vertical stretch and a reflection across the X axe. So we let's write that down. So this will involve a, I'm gonna simplify it down to vs a vertical stretch and a reflection across the X axis. So X axis awesome. So in our second step, we're trying to understand the fact that we're gonna be dealing with a vertical stretch and a reflection across the X axe which will discuss this more in a moment. So our third step is we need to recognize that the coefficient of negative five. So let's underline that. So the coefficient of negative five in front of our G FX function will indicate two things. So a vertical stretch by a factor of five. So the numerical value by itself five will indicate a vertical stretch. So vertical stretch for the five, the coe fish or, or or the numerical value five and a reflection across the X axis because of the negative sign. So because there's a negative sign that will mean that there's a reflection across the x axis. So X axis awesome and don't forget your eye and axis. So once again, the negative five in front of our G FX. So this negative five multiplied by our G FX function will mean the negative sign means that we have a reflection across the X axis. And because we have a five, that means that the five will mean that we'll have a vertical stretch by a factor of five. Awesome. So our fourth and final step is we need to make our final conclusions. So we can conclude that the graph of Y equals negative five multiplied by G FX will look like our original graph of Y equals G FX, but it will be flipped upside down. So we're gonna denote this as Fup. So flipped upside down. So flipped UD. So FD, yeah, so flipped upside down. Awesome. And this is due to the reflection across the X axis. So because of the reflection across the x axis, that means that our graph will be flipped upside down and it will be vertically stretched by a factor of five. So then there's also gonna be a vertical stretch by a factor of five. So by five. Awesome. So that means without a doubt when we look at our multiple choice answers, the correct answer has to be multiple choice answer letter B which states that the graph is reflected across the X axis and is stretched vertically by a factor of five and that's it. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

How do you obtain the graph of $y=-3f\left(x\right)$ from the graph of $y=f\left(x\right)$ ?

Key Concepts

Function Transformation

Vertical Stretch and Reflection

Graphing Techniques

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