Definition of a Function
What is a function?
A function is a rule that assigns to each input exactly one output.
Identify a linear function.
f(x) = 4x - 1 is a linear function.
What is the domain of y = 2x?
The domain is all real numbers.
What does m represent in y = mx + b?
m represents the slope of the line.
Write the standard form of y = 3x + 1.
3x - y = -1 or 3x - y + 1 = 0.
Give an example of a function.
An example of a function is f(x) = 2x + 3.
Identify a nonlinear function.
f(x) = x2 is a nonlinear function.
How does the graph of a linear function look?
It is a straight line.
What does b represent in y = mx + b?
b represents the y-intercept of the line.
Convert y - 2 = 4(x - 1) to slope-intercept form.
y = 4x - 2.
What is the domain of a function?
The domain of a function is the set of all possible input values (x-values).
Provide an example of a linear relationship in real life.
The relationship between distance and time at a constant speed is a linear relationship.
Describe the domain of the function y = x2.
The domain is all real numbers since you can input any real number into the function.
Write the slope-intercept form for a function with a slope of 3 and y-intercept of -2.
The slope-intercept form is y = 3x - 2.
Define point-slope form.
Point-slope form is an equation of the line expressed as y - y1 = m(x - x1) where m is the slope and (x1, y1) is a point on the line.
What is the range of a function?
The range of a function is the set of all possible output values (y-values).
Provide an example of a nonlinear relationship in real life.
The relationship between the area of a circle and its radius is nonlinear.
How does changing the slope affect the graph?
Changing the slope affects the steepness of the line; a larger slope means a steeper line.
Convert y = 2x + 4 to standard form.
The standard form is 2x - y = -4.
Explain how to use point-slope form to write an equation.
To use point-slope form, identify a point on the line and the slope, then plug these values into the formula y - y1 = m(x - x1).
Explain if this is a function: {(1, 2), (1, 3), (2, 4)}.
This is not a function because the input 1 has two different outputs (2 and 3).
Explain why a function is linear or nonlinear.
A function is linear if its graph forms a straight line and can be expressed in the form y = mx + b. It is nonlinear if it cannot be written in this form.
Explain the domain of a linear function with an example.
The domain of a linear function is all real numbers. For example, in the function f(x) = 3x + 2, x can be any real number.
Explain how to find the slope from a graph.
The slope can be found by selecting two points on the line, calculating the rise (change in y) and the run (change in x), and using the formula slope = rise/run.
Write the equation of the line through (2, 3) with a slope of 2 in point-slope form.
The equation is y - 3 = 2(x - 2).