Linear Equations and Modeling
What is the slope and y-intercept of the following line:
-x + 3y = 15
y = (1/3)x + 5
slope = 1/3
y-intercept = (0,5)
Write an equation for a function that has a graph with the shape of |x| but shifted left 2 units and up 5 units.
y = |x + 2| + 5
Is the given equation symmetric with respect to the x-axis, y-axis, and/or the origin?
y = x2 + 3
Symmetric with respect to the y-axis
Given f(x) = -x2 + 3x and g(x) = 3x - 4
Find (fg)(x)
(fg)(x) = -3x3 + 13x2 - 12x
Find the x and y intercepts of the following:
y = -2x - 8
x-intercept = (-4,0)
y-intercept = (0,-8)
Describe the transformations occurring to f(x) in the following:
3f(-x) + 6
f(x) is vertically stretched by a factor of 3, reflected over the y-axis, and shifted up 6 units.
Is the function even, odd, or neither?
f(x) = x3
Odd function
Construct and simplify the difference quotient for the function f(x) = 2x2 - x
4x + 2h - 1
Graph the line y = (2/3)x + 4
Linear graph with a slope of 2/3 and a y-intercept at (0, 4)
The point (2, 4) is on the graph of f(x).
What point is on the graph of -4f(x+1)-3
(1, -19)
Given the following piecewise function:
f(x) = x2 + 3, for x < 2
= 5, for 2 <= x <= 7
= x - 1, for x > 7
Evaluate f(6)
f(6) = 5
Given f(x) = -x2 + 3x and g(x) = 3x - 4
Find (g - f)(1)
(g - f)(1) = -3
A teacher created a linear regression equation using students' hours studied as x, and exam grade as y.
y = 3.4x + 72.8
Find a predicted exam grade for a student who studied for 3 hours.
Where is the following function increasing?
f(x) = (x - 8)2 - 3
Increasing: (8, infinity)
Given the following piecewise function:
f(x) = x2 + 3, for x < 2
= 5, for 2 <= x <= 7
= x - 1, for x > 7
Evaluate f(-4)
f(-4) = 19
Given f(x) = sqrt(x) and g(x) = 2/(x - 4)
Evaluate g(f(4))
g(f(4)) = -1
Find a regression equation for the following data:
x = 3, 7, 5, 9, 4, 10, 8
y= 20, 30, 25, 29, 22, 40, 33
(Round coefficients to three decimal places)
y = 2.404x + 12.630
Where is the following function decreasing?
f(x) = -2|x + 5| + 1
Decreasing: (-5, infinity)
Given the following piecewise function:
f(x) = x2 + 3, for x < 2
= 5, for 2 <= x <= 7
= x - 1, for x > 7
Evaluate f(10)
f(10) = 9
Given f(x) = sqrt(x) and g(x) = 2/(x - 4)
Find f(g(x)) and state its domain.
f(g(x)) = sqrt[2/(x-4)]
Domain = (4, infinity)