Linear Functions
What is the slope and y-intercept of the linear function y = -3x + 7?
Slope (m) = -3, y-intercept (b) = 7 (or (0, 7))
When graphing the inequality y <= 2x - 5, what kind of boundary line do you draw (solid or dashed) and where do you shade (above or below)?
Solid line, shade below.
If a system of two linear equations features parallel lines on a graph, how many solutions does the system have?
No solution (zero solutions).
In the exponential growth function y = 250(1.04)x, what is the initial value (y-intercept) and what is the growth rate as a percentage?
Initial value = 250, Growth rate = 4%
What is the shape of a quadratic function's graph called, and does y = -2x2 + 4x - 5 open up or down?
A parabola; it opens down (because the leading coefficient, -2, is negative).
Find the slope of the line that passes through the points (2, 5) and (4, 11).
m = 3
Solve the inequality: -3x + 7 < 22.
x > -5
Solve the system using substitution:
y = 2x - 3
x + y = 9
(4, 5)
Does the function y = 12(0.85)x represent exponential growth or exponential decay? How do you know?
Exponential decay, because the base (0.85) is between 0 and 1.
What are the coordinates of the vertex for the quadratic function y = (x - 4)2 + 3, and is it a maximum or a minimum?
(4, 3); It is a minimum.
Write the equation of a line in slope-intercept form that has a slope of 2 and passes through the point (3, 1).
y = 2x - 5
Is the point (2, -1) a solution to the inequality 3x - 4y > 10?
No
Solve the system using elimination:
3x + 2y = 10
3x - 2y = 2
(2, 2)
Evaluate the function f(x) = 3(2)x for x = 4.
48
Find the zeros (roots) of the factored quadratic equation 0 = (2x - 5)(x + 3).
x = 5/2 (or 2.5) and x = -3
Convert the standard form equation 4x - 2y = 12 into slope-intercept form.
y = 2x - 6
Solve the compound inequality: -5 <= 2x + 1 < 9.
3 <= x < 4
A classroom test has a total of 25 questions consisting of multiple-choice questions (m) and free-response questions (f). Multiple-choice questions are worth 3 points each, and free-response are worth 8 points each. If the total test is worth 100 points, write the system of equations that represents this scenario.
m + f = 25
3m + 8f = 100
A population of 500 bacteria doubles every hour. Write an exponential function to model the population, P(t), after t hours.
P(t) = 500(2)t (or y = 500 * 2x)
Find the axis of symmetry and the vertex for the function y = x2 - 6x + 8.
Axis of symmetry: x = 3; Vertex: (3, -1)
Write the equation of a line that passes through (1, 4) and is perpendicular to the line y = -1/3x + 9.
y = 3x + 1
Write a linear inequality to match this scenario: You have a $50 gift card to spend on movie tickets (x) which cost $10 each and snacks (y) which cost $5 each.
10x + 5y <= 50 (or any equivalent form)
Solve the following system of equations using any method:
2x + 3y = 11
4x - y = 1
(1, 3)
You deposit $1,000 into a savings account that earns 5% interest compounded annually. Write the explicit equation to find the balance after t years, and determine if the domain can include negative numbers in this context.
A(t) = 1000(1.05)t. No, the domain cannot include negative numbers because time cannot be negative in this scenario (t >= 0).
Solve the quadratic equation x2 - 5x - 14 = 0 by factoring.
x = 7 and x = -2