Functions
f(x) = 2x + 3
g(x) = 3x + 2 +x2
Find f(5)
f(5) = 13
If m = 4, what is the perpendicular slope?
m = -1/4
Write the shift or transformation of the following equation: y = (x-2)2
Horizontal shift: 2 to the right
If f(x) = 2x + 3 and g(x) = 3x + 3
Find (f+g)(x)
(f+g)(x) = 5x + 6
If f(x) = (3,4) and (5,8)
Find f-1(x)
f-1 = (4,3) and (8,5)
f(x) = 2x + 2
g(x) = x2-4x+2
Find g(4)
g(4) = 2
Find the slope: (2,3) (4,2)
m = -1/2
Write the shift or transformation of the following equation:
y = 3f(x+3)2 - 3
Horizontal shift is 3 to the left
Vertical shift is 3 down
Vertical stretch of 3
If f(x) = 5x + 4 and g(x) = 4x + 3
Find (f - g)(x)
(f-g)(x) = x + 1
Does y = x2 - 5 pass or fail the horizontal line test and why?
It fails the horizontal line test because it hits graph more than once horizontally meaning that it's not an inverse function.
f(x) = {2x + 1, x < 2
3x, 2 ≤ x ≤ 4
x2 + 2x + 3,} x > 4
Find f(3), f(-2), f(7), and f(2)
f(3) = 9
f(-2) = -3
f(7) = 66
f(2) = 6
Write the point-slope form through the line (3,4) when the slope is 2
y - 4 = 2(x - 3)
Find the domain of the following function:
f(x) = √x-2
The domain is x ≥ 2
If f(x) = 2x + 2 and g(x) = 4x + 1
Find f(g(x))
f(g(x)) = 8x + 4
Find the inverse of the following equation:
y = 4x - 2
x/4 + 1/2 = y
f(x) = x3 + 5x
g(x) = x2-4x
Find f(3) and g(2)
f(3) = 42
g(2) = -4
Write the point-slope form through the line (2,6) and is parallel to the line 9x - 3y = 5
y - 6 = 3(x - 2)
The coordinates of a graph are (-5,0), (-3,1), (0, 4) and (4,2)
Find the Domain and Range of the following graph
Domain = -5 ≤ x ≤ 4
Range = 0 ≤ y ≤ 4
If f(x) = x2 - 2x - 63 and g(x) = 5x2 - 4x + 5
Find (g/f)(x) and the Domain
(g/f)(x) = 5x2 - 4x + 5 / 3x2 - 3
Domain of (g/f)(x): x ≠ 9 , -7
Find the inverse of the following equation:
y = (x-5)1/3
x3 + 5 = y
5/x2 -3
Find f(4)
f(4) = 5/13
Write the point-slope form through the line (2,8) and is perpendicular to the line 5x + 20y = 5
y - 8 = 4(x - 2)
Does the graph y = -(x-3)2 have a min and a max? If it does, state the max and/or min
The graph y = -(x-3)2 has a max of (3,0)
The graph does not have a min
If f(x) = 3x + 4 and g(x) = 5x + 2
Find (f+g)(x+4)
(f+g)(x+4) = 8x + 38
Find the inverse of the following equation:
y = (5x + 6)3
x1/3/5 - 6/5 = y