About Additional Graphs of Functions:

When graphing elementary functions, we are often asked to find the horizontal and/or vertical transformation. We can find the horizontal shift based on what happens inside of our function. We can find the vertical shift based on what happens outside of our function.


Test Objectives
  • Demonstrate the ability to sketch the graph of an elementary function with a transformation
  • Demonstrate the ability to find the horizontal shift of an elementary function
  • Demonstrate the ability to find the vertical shift of an elementary function
Additional Graphs of Functions Practice Test:

#1:

Instructions: Find the shift based on the function given.

$$f(x) = |x|$$

a) $$f(x) = |x - 11|$$

b) $$f(x) = |x - 24|$$

c) $$f(x) = |x| + 9$$

d) $$f(x) = |x| + 12$$

e) $$f(x) = |x - 3| + 7$$


#2:

Instructions: Find the shift based on the function given.

$$f(x) = |x|$$

a) $$f(x) = |x - 13| + 4$$

b) $$f(x) = |x - 10| + 8$$

c) $$f(x) = |x + 7| + 1$$

d) $$f(x) = |x + 14| - 8$$

e) $$f(x) = |x + 11| - 11$$


#3:

Instructions: Find the shift based on the function given.

$$f(x) = \frac{1}{x}$$

a) $$f(x) = \frac{1}{x} + 1$$

b) $$f(x) = \frac{1}{x - 13}$$

c) $$f(x) = \frac{1}{x} - 7$$

d) $$f(x) = \frac{1}{x + 11}$$

e) $$f(x) = \frac{1}{x} - 12$$


#4:

Instructions: Find the shift based on the function given.

$$f(x) = \sqrt{x}$$

a) $$f(x) = \sqrt{x - 2}$$

b) $$f(x) = \sqrt{x + 7}$$

c) $$f(x) = \sqrt{x} - 2$$

d) $$f(x) = \sqrt{x + 4} - 3$$

e) $$f(x) = \sqrt{x - 9} - 5$$


#5:

Instructions: Find the shift based on the function given.

$$f(x) = [\![x]\!]$$

a) $$f(x) = [\![x - 7]\!]$$

b) $$f(x) = [\![x + 3]\!]$$

c) $$f(x) = [\![x]\!] - 4$$

d) $$f(x) = [\![x]\!] - 1$$

e) $$f(x) = [\![x - 5]\!] - 9$$


Written Solutions:

#1:

Solutions:

a) Shifts 11 units right

b) Shifts 24 units right

c) Shifts 9 units up

d) Shifts 12 units up

e) Shifts 3 units right and 7 units up


#2:

Solutions:

a) Shifts 13 units right and 4 units up

b) Shifts 10 units right and 8 units up

c) Shifts 7 units left and 1 unit up

d) Shifts 14 units left and 8 units down

e) Shifts 11 units left and 11 units down


#3:

Solutions:

a) Shifts 1 unit up

b) Shifts 13 units right

c) Shifts 7 units down

d) Shifts 11 units left

e) Shifts 12 units down


#4:

Solutions:

a) Shifts 2 units right

b) Shifts 7 units left

c) Shifts 2 units down

d) Shifts 4 units left and 3 units down

e) Shifts 9 units right and 5 units down


#5:

Solutions:

a) Shifts 7 units right

b) Shifts 3 units left

c) Shifts 4 units down

d) Shifts 1 unit down

e) Shifts 5 units right and 9 units down