Quiz about linear Transformations

Question 1

The graphs of linear functions f and g are shown on the grid. Which function is best represented by the graph of g?

Accepted Answer

$$g\left(x\right)=f\left(x\right)+3$$

Answer

$$g\left(x\right)=f\left(x\right)-3$$

Answer

$$g\left(x\right)=3f\left(x\right)$$

Answer

$$g\left(x\right)=-3f\left(x\right)$$

Question 2

The graphs of linear functions f and g are shown on the grid.

Which function is best represented by the graph of g?

Accepted Answer

$$g\left(x\right)=3f\left(x\right)$$

Answer

$$g\left(x\right)=f\left(x\right)+4$$

Answer

$$g\left(x\right)=f\left(x\right)+5$$

Answer

$$g\left(x\right)=\frac{1}{3}f\left(x\right)$$

Question 3

What does the equation

$$g\left(x\right)\ =\ f\left(x\right)-4\ $$ do to the graph of f(x)?

Accepted Answer

Shifts the graph down four units

Answer

Shifts the graph left four units

Answer

Shifts the graph right four units

Answer

Shifts the graph up four units

Question 4

Which transformation on

f(x) = x

is g(x) = -f(x)

Accepted Answer

Reflection across the x-axis.

Answer

Reflection across the y-axis

Answer

The slope will be less steep

Answer

The graph will be wider

Question 5

The linear parent function, f(x) = x, is transformed to g(x) = f(x) - 6. Describe the transformation.

Accepted Answer

g(x) is shifted down 6 units

Answer

g(x) is shifted up 6 units

Answer

g(x) is shifted left 6 units

Answer

g(x) is shifted right 6 units

Question 6

$$f\left(x\right)=x$$ and $$g\left(x\right)=2x-4$$
Which statement about the relationship of these two graphs is true?

Accepted Answer

The graph of g is steeper than the graph of f, and the y-intercept has been translated down.

Answer

The graph of g is steeper than the graph of f, and the y-intercept has been translated up.

Answer

The graph of g is less steep than the graph of f, and the y-intercept has been translated up.

Answer

The graph of g is less steep than the graph of f, and the y-intercept has been translated down.

Question 7

$$f\left(x\right)=x$$ and $$g\left(x\right)=-\frac{2}{3}x$$
Which statement about the relationship between these two graphs is true?

Accepted Answer

The graph of g is less steep than the graph of f, and is reflected.

Answer

The graph of g is less steep than the graph of f.

Answer

The graph of g is reflected, and the y-intercept is translated down.

Answer

The graph of g is steeper than the graph of f, and is reflected.

Question 8

The linear parent function, f(x) = x, is transformed to g(x) = f(x + 3). Describe the transformation.

Accepted Answer

g(x) is shifted left 3 units

Answer

g(x) is shifted up 3 units

Answer

g(x) is shifted down 3 units

Answer

g(x) is shifted right 3 units

Question 9

The linear parent function, f(x) = x, is transformed to g(x) = f(x - 6). Describe the transformation.

Accepted Answer

g(x) is shifted right 6 units

Answer

g(x) is shifted up 6 units

Answer

g(x) is shifted down 6 units

Answer

g(x) is shifted left 6 units

Question 10

How did the equation shift from the parent function? y = f(x + 7)

Accepted Answer

Left 7

Answer

Up 7

Answer

Down 7

Answer

Right 7

Question 11

Let g(x) be the indicated transformation of f(x). Write the rule for g(x).

f(x)= - 3x + 6, vertical translation up 9 units

Accepted Answer

g(x)= - 3x + 15

Answer

g(x)= - 3x - 21

Answer

g(x)= - 3x + 33

Answer

g(x)= - 3x - 3

Question 12

Let g(x) be the indicated transformation of f(x). Write the rule for g(x).

f(x)= - 8x - 3, vertical translation down 5 units

Accepted Answer

g(x)= - 8x - 8

Answer

g(x)= - 8x + 2

Answer

g(x)= - 8x + 37

Answer

g(x)= - 8x - 44

Question 13

Let g(x) be the indicated transformation of f(x). Write the rule for g(x).

f(x)= 12x + 18, vertical stretch by a factor of 3

Accepted Answer

g(x)= 36x + 54

Answer

g(x)= 4x + 6

Answer

g(x)= 36x + 18

Answer

g(x)= 4x + 18

Question 14

Let g(x) be the indicated transformation of f(x). Write the rule for g(x).

f(x)= - 9x + 12, reflect across the y-axis

Accepted Answer

g(x)= 9x +12

Answer

g(x)= 9x - 12

Answer

g(x)= - 9x - 12

Answer

g(x)= - 9x + 12

Question 15

Accepted Answer

vertical stretch factor 2 and translate up 3

Answer

vertical stretch factor 2 and translate left 3

Answer

vertical stretch factor 2 and translate down 3

Answer

translate right 2 and up three

Question 16

Accepted Answer

reflect over x axis and horizontal stretch by 2.

Answer

reflect over x axis and vertical stretch by 2.

Answer

reflect over y axis and vertical stretch by 2.

Answer

reflect over y axis and horizontal stretch by 1/2.

Question 17

Accepted Answer

translate six right and 7 up

Answer

translate six left and 7 up

Answer

translate six right and 7 down

Answer

translate six left and 7 down

Question 18

Accepted Answer

vertical shrink factor 1/4, reflect over y-axis, translate down 1

Answer

vertical stretch factor 1/4, reflect over x-axis, translate down 1

Answer

vertical shrink factor 1/4, reflect over x-axis, translate down 1

Answer

horizontal shrink factor 4, reflect over y-axis, translate down 1

linear Transformations

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