Linear Transformations

Given f(x)= 5x+2, describe the transformation:

g(x) = 2(fx)

• Vertical stretch

• Vertical compression

• Horizontal stretch

• Horizontal compression

Answer explanation

The function g(x) = 2(f(x)) indicates a vertical stretch of the original function f(x) = 5x + 2 by a factor of 2. This means that the output values of f(x) are multiplied by 2, resulting in a vertical stretch.

Tags

CCSS.HSF.BF.B.3

• Vertical stretch

• Vertical compression

• Horizontal stretch

• Horizontal compression

Answer explanation

The transformation g(x) = f(1/3 x) indicates a horizontal stretch. The factor of 1/3 means that for every x-value, the corresponding output is stretched, making the graph wider.

Tags

CCSS.HSF.BF.B.3

• Vertical stretch

• Vertical compression

• Horizontal stretch

• Horizontal compression

Answer explanation

The transformation g(x) = f(4x) compresses the graph horizontally by a factor of 4. This means that for every x-value, the corresponding y-value occurs at a quarter of the original x-distance, resulting in horizontal compression.

Tags

CCSS.HSF.BF.B.3

• Vertical stretch

• Vertical compression

• Horizontal stretch

• Horizontal compression

Answer explanation

The transformation g(x) = (1/5)f(x) indicates a vertical compression. The factor 1/5 compresses the output values of f(x) towards the x-axis, making the graph shorter vertically.

Tags

CCSS.HSF.BF.B.3

Describe the transformation that occurred

p(x) = f(x + 3)

• Right 3 units

• Vertical Stretch

• Up 3 units

• Left 3 units

Answer explanation

The transformation p(x) = f(x + 3) indicates a horizontal shift. Since we are adding 3 inside the function, it shifts the graph left by 3 units. Thus, the correct answer is 'Left 3 units'.

Tags

CCSS.HSF.BF.B.3

Describe the transformation that occurred.

h(x) = f(x) + 2

• up 2 units

• left 2 units

• Vertical Strech

• right 2 units

Answer explanation

The transformation h(x) = f(x) + 2 indicates a vertical shift of the function f(x) upwards by 2 units. Therefore, the correct choice is 'up 2 units'.

Tags

CCSS.HSF.BF.B.3

Describe the transformation that occurred

m(x) = f(x + 1)

• Left 1 Unit

• Right 1 unit

• vertical stretch

• up 1 unit

Answer explanation

The transformation m(x) = f(x + 1) indicates a horizontal shift. Since we are adding 1 to x, the graph shifts left by 1 unit. Therefore, the correct answer is 'Left 1 Unit'.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

Describe the transformation that occurred.

w(x) = f(x - 7)

• Down 7

• Up 7

• Right 7

• vertical compression

Answer explanation

The transformation w(x) = f(x - 7) indicates a horizontal shift. Specifically, the function f(x) is shifted to the right by 7 units. Thus, the correct choice is 'Right 7'.

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

If the graph of the parent function f(x) = x is shifted 7 units
down, which of the following equations would the new graphed
line represent?

• f(x) = 7x

• f(x) = x - 7

• f(x) = x + 7

• f(x) = 7x - 7

Answer explanation

Shifting the graph of f(x) = x down by 7 units means subtracting 7 from the function. Thus, the new equation is f(x) = x - 7, which correctly represents the downward shift.

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Which equation would represent a move of 2 units up for parent function f(x) = 7x

• g(x) = 9x

• g(x) = 7x + 2

• g(x) = 7(x+2)

• g(x) = 7(x-2)

Answer explanation

To move the function f(x) = 7x up by 2 units, we add 2 to the output. Thus, the correct equation is g(x) = 7x + 2, which represents this vertical shift.

Tags

CCSS.HSF.BF.B.3