Shifting Graphs

Exercises 27...

Question

Shifting Graphs

Exercises 27–36 tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation.

y = (1/2)(x + 1) + 5 Down 5, right 1

Accepted Answer

Write the new equation after shifting the given graph as stated below. Also, plot both graphs using the same rectangular coordinate system, where we have Y equals 1/3, multiplied by X minus 5 + 2. Our transformation is down 2 units and right 3 units, and we're also given a graph to graph our equations on. Now to solve this, we'll first apply our transformations. You have Y equals 1/3, X minus 5 + 2. Now, to apply our transformations, we first have A vertical shift of down 2 units. This means that we will subtract to from our equation. That gives us + 2 minus 2 at the end. Which gives us 1/3 multiplied by X minus 5. Now, we're going to shift this right. By 3 units This means we'll replace X with X minus 3, giving us Y equals 1/3. X minus 3. -5 Which gives us 1/3 X minus 8. Now this is the equation of our transformation. And now we need to grab both of our equations. Let's find the intercepts. The X intercept we let. Y equals 0. We have 0 equals 1/3, multiplied by X minus 8. Which gives us 0 equals. X minus 8 And then if we add 8 to both sides, we get X equals 8, giving us a point of 80. We can also do the same for the Y intercepts. By letting X equals 0. Y equals 1/3, multiplied by 0 minus 8. Which gives us 1/3 multiplied by 8 or 83. This means our Y intercept will be at the point 0-83. Let's also get the graph of our original function. 1/3 X minus 5 plus 2. Our X intercepts we will once again. Let Y equals 0. Giving us 0 equals 1/3, multiplied by X minus 5 + 2. We subtract 2 from both sides. First, we get -2 equals 1/3, multiplied by X minus 5. And we can multiply both sides by 3 to get -6 equals X minus 5. Finally, add 5. To get X equals -1 and the points of -10. With the Y in set, we let X equals 0. We have Y equals 1/3, 0 minus 5, plus 2. Which gives us 1/3 multiplied by 5 plus 2. Or ate the 5/3 + 2. Which simplifies to 1/3, giving us a point of 0, 1/3. We can now graph both equations on our graph. For our original, we have 2 points at -10 and 0 1/3. So, -10. And 0 1/3. This will give us Our first equation Now We can also graph our other equation. We have the points. 80 And we have the point. 0, 8/3. And we draw a line between the two points. This gives us our other graph. Being Y equals 1/3 X minus 8s. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

Key Concepts

Graph Shifting

Linear Equations

Coordinate Plane

Watch next

Shifting GraphsExercises 27–36 tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation.y = (1/2)(x + 1) + 5 Down 5, right 1

Key Concepts

Graph Shifting

Linear Equations

Coordinate Plane

Watch next