Absolute Value Graphs
What are the h and k values of the function f(x) = ∣x + 2 ∣ − 3 ?
(-2, -3)
h = -2
k = -3
Write an equation of the line with the given slope and y-intercept.
Slope: 2
Y-intercept: 9
y = 2x + 9
What kind of slopes do parallel lines have?
same slopes
What is the purpose of an inverse function?
To "undo" the original function.
Describe the transformations from the graph of f(x) = ∣x∣ to the graph of g.
g(x) = ∣x − 1∣ + 3
1 unit right, 3 units up
Write an equation of the line in slope-intercept form.
(see graph)
y = 1/4x + 3
What kind of slopes do perpendicular lines have?
opposite reciprocal slopes
What are the two steps to finding an inverse function?
1. Switch the x and y
2. Solve for y
Describe the transformations from the graph of f(x) = ∣x∣ to the graph of the given function.
r(x) = ∣x + 2∣ − 6
2 units left, 6 units down
Describe and correct the error in writing an equation of the line with a slope of 2 and a y-intercept of 7.
y = 7x + 2
The correct equation would be y = 2x + 7
What is the opposite reciprocal of -2?
1/2
Solve the below equation for y.
x = 7y - 21
x/7 + 3 = y
Describe the transformations from the graph of f(x) = ∣x∣ to the graph of the given function.
d(x) = −∣x − 3∣ + 5
3 units right, 5 units up, facing down
Write a linear function f with the given values.
f(0) = 2, f(2) = 4
y = x + 2
Determine if the lines are parallel, perpendicular, or neither.
y = -5x + 4
y = 1/5x + 4
Perpendicular
Find the inverse function for y = 3x - 9
x/3 + 3 = y
Write an equation that represents the given transformations of the graph of f(x) = ∣x∣.
vertical translation 7 units down
f(x) = ∣x∣ - 7
Write an equation of the line that passes through the given points.
(3, 1), (0, 10)
y = -3x + 10
Determine if the lines are parallel, perpendicular, or neither.
Line a passes through (−1, 3) and (1, 9).
Line b passes through (−2, 12) and (−1, 14)
Neither
Find the inverse function for y = 1/2x + 4
2x - 8 = y