Horizontal Shifts 2

Horizontal Shifts 2

Please go through the slides and videos and practice problems!

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A horizontal shift occurs when we add or subtract a quantity from the input of the function. Remember, with horizontal shifts, it is actually opposite of what you may think. 

Describe what is happening to the function, use the red sentence to help you come up with a full sentence response.

f(x) ----> g(x) = f(x - 2)

 

The transformation from f to g is a horizontal shift ____________ units _______________.

Shifting Right

When we shift a linear equation horizontally in the positive direction aka "right", we are subtracting from the input.

For example;

If f(x) = 2x + 3 and g(x) = f(x-4) then we are shifting the function f 4 units to the right.

Please watch this video explanation.

Shifting Left

When we shift a linear equation horizontally in the negative direction, aka left, we are adding to the input.

For example;

If f(x) = -5x + 5 and g(x) = f(x+3) then we are shifting the function f 3 units to the left.

Please watch this video explanation.

Main Points

• When you shift a function horizontally, you are adding to or subtracting from the input.

• Adding to the input of a function will shift the original function horizontally to the left

• Subtracting from the input of a function will shift the original function horizontally to the right.

• f(x) ----> f(x + 3) Shifts the funtion 3 units to the left.

• f(x) ----> f(x - 4) Shifts the function 4 units to the right.

Multiple Choice

If f(x) = 3x - 2 and h(x) = f(x + 8) how would you describe the graph of h compared to the graph of f?

• The graph of h is the image of the graph of f shifted 8 units to the right.

• The graph of h is the image of the graph of f shifted 8 units to the left.

Multiple Choice

f(x) = 3x + 5

Describe how the graph of g compares with the graph of f.

g(x) = 3(x-2) + 5

• The graph of g has the same slope as f, and is shifted 2 units to the right of f.

• The graph of g has a different slope then f, and is shifted 2 units to the right of f.

• The graph of g has a different slope from f, and is shifted 2 units to the left of f.

• The graph of g has the same slope as f, and is shifted 2 units to the left of f.

Multiple Choice

f(x) = 3x + 5

Describe how the graph of g compares with the graph of f.

g(x) = 3(x + 3.5)

• The graph of g has the same slope as f, and is shifted 3.5 units to the right of f.

• The graph of g has a different slope from f, and is shifted 3.5 units to the right of f.

• The graph of g has the same slope as f, and is shifted 3.5 units to the left of f.

• The graph of g has a different slope from f, and is shifted 3.5 units to the left of f.

Multiple Choice

If g is a horizontal translation of f, what is the value of h?

f(x) = 2x - 6

g(x) = 2(x + h) - 6

• -8

• 8

• -4

• 4

Multiple Choice

If g is a horizontal translation of f, what is the value of h?

 $f\left(x\right)=\frac{1}{3}x+2$  (red line)
 $g\left(x\right)=\frac{1}{3}\left(x+h\right)\ +\ 2$ (blue line) 

• 5

• -5

• -6

• -1

Multiple Select

Which of the following would shift the graph of f to the left? Select all that apply.

f(x) = -4x + 1

• g(x) = f(x - 2)

• g(x) = f(x + 2)

• g(x) = -4(x -2) + 1

• g(x) = -4(x + 2) +1

Open Ended

How does modifying the input or the output of a linear function rule transform the graph?

Poll

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