Functions
What is a relation?
A set of Inputs paired with Outputs
How can you change an equation to be written in function notation? (2 Steps)
1. Solve for y
2. Change y to f(x)
What is the standard form of linear equations?
Ax + By = C
What are a family of functions and what is a parent function?
A Family of Functions is a group of functions with similar characteristics.
The most basic function in a family of functions is the parent function.
What is the parent function of all Absolute Value Functions?
f(x) = |x|
or
y = |x|
What makes a function different than a relation?
Every Input in a functions only has one unique output
What does f(x) represent in a function?
Represents the output of function f corresponding to the input x
What is slope intercept form and what do each of the letters represent?
y = mx + b
y = output, x = input, m = slope, b = y-intercept
What is the parent function of all Linear Functions?
f(x) = x
or
y = x
What is the vertex of an absolute value function?
Identify the Domain and Range of the following function: {(1, 2), (5, - 4), (0, -2), (-3, 4), (-7, 7)}
Domain: {-7, -3, 0, 1, 5}
Range: {-4, -2, 2, 4, 7}
f(11) = 2 * 11 + 6
f(11) = 22 + 6
f(11) = 28
What is the x and y intercept of the function 5x + 4y = 20?
y-intercept: (0, 5)
What is a transformation? And what are the four different types?
A transformation changes the size, shape, position, or orientation of a graph.
Translation, Reflection, Stretches, and Shrinks
What is the vertex form of absolute value functions? And what does each letter represent?
f(x) = a |x - h| + k
f(x) = output
x = input
h = x-coordinate of vertex
k = y-coordinate of vertex
a = the magnitude of the slope of each lines in the graph
Imagine we are studying the relation between the number of hours students study and their test scores: What is the Independent Variable and what is the Dependent Variable?
Independent: Hours students spent studying
Dependent: Test scores
x = 5
What is slope and how do you calculate it?
Slope is the rate of change between any two points on a line.
m = rise/run = (y2 - y1)/(x2 - x1)
Describe the transformation of 3 * f(x - 2)
Horizontal shift of 2 units to the right and a vertical stretch by a factor of 3.
What is the domain and range of the function f(x) = |x| + 2
Domain: All Real Numbers
Range: y >= 2
What's the difference between a discrete domain and a continuous domain?
A discrete domain is a set of input values that consists of only certain numbers in an interval.
And a continuous domain is a set of input values that consists if all numbers in an interval.
Let f(t) be the outside temperature t hours after 6 am. Explain the meaning of this statement. f(5) = 78 AND f(5) > f(2)
The temperature at 11am was 78 and this was greater than the temperature at 8am
What is the slope and y-intercept of the following equation: 2y - 8x = - 6 ?
Slope = 4
y-intercept = - 3
Describe the transformation of the function y = -x + 6
Reflection over the x-axis and a upward shift of 6 units
What is the vertex of the function f(x) = 3|x + 2| + 4
(-2, 4)