Functions
f(x) = {(-2,0), (-1,0), (0,1), (1,1), (2,2), (3,2)}
f(0) = ?
Write your answer in function notation.
f(0) = 1
Absolute value function
f(x)= |x|
The absolute value function has been shifted to the left 5 and down 2 units. Write the equation of the new function, using correct function notation.
f(x)= |x+5| - 2
Is the following relation a function?
x: 0 1 2 4 2 7 8 10
f(x): 5 1 -2 1 0 -3 0 9
No, the relation is not a function. The input 2 has two different outputs.
Write the vertex and axis of symmetry for the following graph. Use proper notation for both.
Vertex: (4,-3)
Axis of symmetry: x = 4
x: 0 1 2 4 2 7 8 10
g(x): 5 1 -2 1 0 -2 0 9
Find the x-value(s) so that g(x) = -2.
x = 2 and x = 7
State the name and equation of the parent function transformed to create the new function
f(x)= -(1/2)x - 3
Linear function
f(x)=x
The square root function has been reflected across the y-axis, and dilated vertically by a factor of 1/2. Write the equation of the new function, using function notation.
f(x)= (1/2)sqrt(-x)
Is the following relation a function? Explain why or why not.
{(-2,0), (-1,0), (0,1), (1,1), (2,2), (3,2)}
Yes, the relation is a function. Every input has only one output.
Write the domain and range of the following graph.
D: [2, infinity)
R: [1, infinity)
h(x) = 2|x - 1|
Find h(-2).
Write your answer in function notation.
h(-2) = 6
State the name and equation of the parent function transformed to create the new function
g(x)= 3/(2x)
Rational function
f(x)= 1/x
Vertical stretch x3
Shift left 1
Shift up 2
Is this relation a function? If it is a function, is it continuous?
x: 0 1 4 2 7 8 10
f(x): 1 -1 -3 -5 -7 -9 -11
Yes, this relation is a function. No, this function is not continuous.
Write the intervals of increase and decrease of the following graph, in terms of x-values.
Increasing: (-infinity, -4)
Decreasing: (-4, infinity)
f(x) = -x2 - 3 g(x) = 4x + 1
Find f(-1) + g(3).
f(-1) + g(3) = 9
The function g(x) is a parent function, and it does not have an interval of decrease on its domain. Of the 6 we have discussed, what are the names of all the possible parent functions for g(x)? (You must name all to receive points)
Linear, Square Root, or Cubic function.
State the transformations done to the parent function to create the function g(x)= (-2x)3. (You must list all transformations correctly to receive points)
Reflection across the y-axis
Horizontal compression x1/2
What is the domain of the following relation?
{(-2,0), (-1,0), (0,1), (1,1), (2,2), (3,2)}
D: {-2, -1, 0, 1, 2, 3}
In the following graph, what is the greatest rate of change? Include units in your answer.
400 people per hour
Find the x-intercept(s) of h(x). Write your answer(s) as a coordinate pair.
(0, 0) and (2, 0)
The function h(x) is a parent function, and it has a range of all real numbers. Of the six we have discussed, what are the possible functions for h(x). (You must name all to receive points)
Linear or Cubic function.
Use your knowledge of parent functions and transformations to write the equation of the following graph.
f(x)= -|x - 2| + 1
What are the x-intercept(s) of following relation? Write your answer(s) as a coordinate pair.
x: 0 1 2 4 2 7 8 10
f(x): 5 1 -2 1 0 -3 0 9
(2,0) and (8,0)
The following graph represents the function P(t), which describes the distance Anthony is from his house as he runs errands. Find the t-value(s) where P(t)= 3, and write a sentence to interpret your answer in the context of the problem. Include units in your interpretation.
t= 1 and 19
At the 1st minute and the 19th minute of Anthony's errand run, he is 3 blocks away from his house.