SECOND TERM QUIZ REVIEW

1.  Which transformation will occur if f(x) = x is replaced by g(x) = x + 9?

• translation left 9 units

• translation right 9 units

• reflection across the x-axis

• vertical translation up 9 units

Answer explanation

Translation up k units, k > 0  g(x) = f(x) + k

What would be the equation of f(x) given that g(x) = x + 8 has a vertical shift of 8?

• f(x) = x

• f(x) = 8x

• f(x) = -8x

• f(x) = x + 8

Answer explanation

Translation up k units, k > 0  g(x) = f(x) + k

Given f(x) = x + 5 and g(x) = 3x + 5. What is true to these equations?

• The graph of f is a horizontal stretch of the graph of g by a scale factor of 3 through the y-axis.

• The graph of g is a horizontal compression of the graph of f by a scale factor of 3.

• The graph of g is a vertical compression of the graph of f by a scale factor of 3.

• The graph of f is a vertical stretch of the graph of g.

Answer explanation

Multiplying the input of a linear function f by k scales its graph horizontally.

k > 1, the transformed graph is a horizontal compression.

What happens to the graph of a linear function If you add or subtract a constant from the input?

• The function will be stretched.

• The function will be compressed.

• The function will be shifted vertically.

• The function will be shifted horizontally.

Answer explanation

Horizontal Translation:

Translation to the right k units, k > 0  g(x) = f(x – k).

Translation to the left k units, k > 0  g(x) = f(x + k).

Which function is a vertical translation of the linear parent function f(x) = x?

• g(x) = 2x

• g(x) = -2x

• g(x) = x + 14

• g(x) = 2x + 14

Answer explanation

Vertical Translations:

Translation up k units, k > 0  g(x) = f(x) + k.

Translation down k units, k > 0

g(x) = f(x) – k.

What would the equation be of f(x) = 4x – 2 if the function was translated to 4 units left?

• g(x) = 3x - 4

• g(x) = 4x + 3

• g(x) = 4(x – 4) – 2

• g(x) = 4(x + 4) – 2  

Answer explanation

Horizontal Translation:

Translation to the right k units, k > 0  g(x) = f(x – k).

Translation to the left k units, k > 0  g(x) = f(x + k).

Which is true for the graphs of f (black) and g (red)?

• vertical translation down 9 units

• vertical translation down 9 units

• vertical stretch 9 units

• vertical compression 9 units

Answer explanation

Vertical Translation:

Translation up k units, k > 0  g(x) = f(x) + k.

Translation down k units, k > 0  g(x) = f(x) – k.

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

• shifted down 7 units

• dilated 7 units

• shifted up 7 units

• compressed 7 units

Answer explanation

Vertical Translation:

Translation up k units, k > 0  g(x) = f(x) + k.

Translation down k units, k > 0  g(x) = f(x) – k.

Which transformation of f(x) (black) to g(x) (red)is true?

• left 5 units

• up 4 units

• right 4 units

• down 4 units

Answer explanation

Vertical Translation:

Translation up k units, k > 0  g(x) = f(x) + k.

Translation down k units, k > 0

g(x) = f(x) – k.

Answer explanation

Vertical Compression:

Multiplying the output of a linear function f by k scales its graph vertically.

0 < |k| < 1 the transformed graph is a vertical compression.