Transformations
Inverses
Parametric
Graphs
Functions
100
What is an equation for the squaring function shifted up by 2?
f(x) = x^2 + 2
100
What is an equation for the inverse of the function
f(x) = 5x?
f(x) = x/5
100
f(t) = (2t, t2)
Find f(-2)
f(-2) = (-4, 4)
100
For the graph below, write the domain and range in interval notation:
Domain: x ∈ (-∞, ∞)
Range: y ∈ [-3, ∞)
100
Is the following relation a function:
{(1,3), (2,4), (3,4)} ?
Explain.
yes
200
What is an equation for the absolute value function shifted to the left by 20?
f(x) = |x + 20|
200
What is the equation for the inverse of the function f(x) = 7x + 1?
f(x) = (x – 1)/7
200
Let f(t) = (3cost, ln(t ) = 3) 0< t < 10
Find x(t) and y(t)
200
Given the graph below, find:
1. f(-1)
2. Find the x value when f(x) = -2
f(-1) = -2
when f(x) = -2, x = -1 and x = 2
200
Does the graph below represent a function? Explain.
yes. vertical line test
300
What is an equation for the exponential function scaled vertically by a factor of 4 and reflected across the y-axis?
f(x) = 4(e^–x)
300
Find the inverse f -1(x) of:
f(x) = (x + 2)2 + 3
f-1(x) = √(x - 3) - 2
300
At time t = -3, where is the parametric function
f(t) = (t2 + 3, 1/t )
f(-3) = (12, - 1/3)
300
For the graph below, identify the intervals on which the function is increasing and decreasing:
Increasing: x ∈ (-1, 1)
Decreasing: x ∈ (-∞, -1) U (1, ∞)
300
Given f(x) = 3x-2 and g(x) = -x , find f(g(-4)).
f(g(-4)) = 10
400
What is an equation for the cubing function shifted up by 5, to the right by 4, and reflected across the x-axis?
f(x) = – [(x – 4)^3 + 5]
400
What is the equation for the inverse of the function f(x) = 2 + 3/x?
f(x) = 3/(x - 2)
400
Find the domain of the parametric function.
f(t) = (1/t , sqrt(t - 2))
t>2
400
Graph the piecewise function:
*check with DESMOS
400
If f(x) = -x2 + 3x and g(x) = x - 1, find f(g(x)). Simplify your answer.
f(g(x)) = -x2 + 5x - 4
500
What is an equation for the function f(x) = 3x – 2 after it is reflected across the y = x line?
f(x) = (x + 2)/3
500
Given: f(x) = -x3 - 3 and g(x) = ∛(-x - 3).
Are f(x) and g(x) inverses of one another? Explain.
Yes, f(g(x)) = g(f(x)) = x
500
What is the x-intercept and y-intercept of the parametric function:
f(t) = [(t-1, t2-4)]
x - intercept at t= 2, -2 (1,0) and (-3,0)
y -intercept at t=1. (0, -3)
500
Find the vertical and horizontal asymptote.
f(x) = x / (x - 5)
VA: x =5
HA: y = 1
500
Write the pair of parametric equations in rectangular form and find the domain.
x(t) = t - 1
y(t) = 2t2 -1 < t < 6
f(x) = y = 2(t-1)2 -2<x<5