Definitions
What is a reflection?
A type of transformation that flips a graph over a line called the line of reflection.
Identify the parent function. Then, describe transformations.
f(x) = x + 2
1. Linear
2. Shift Up by 2
f(x) = 3x - 1. Write a function g whose graph is a translation 5 units up.
What is the slope equation?
m = y2-y1 / x2-x1
How do you determine if a set of data is linear?
If the values are one-to-one / plot it and draw a line of fit.
A transformation is a change in ______ , ______, ______, ______, of a graph.
A change in size, shape, position, or orientation of a graph.
Identify the parent function. Then, describe transformations.
f(x)=|x+4| - 1
1. Absolute Value
2. Shift LEFT 4, DOWN 1
f(x) = |x-3|+4. Write a function g whose graph is a reflection in the x-axis.
g(x) = - |x+3|+4
A given graph has a slope of 2.5 and a point at (4, 10). Find the y-intercept.
The y-intercept is (0,4)
A line of best fit was calculated for data representing the number of hours studied (x) and the test scores (y). Using the equation, interpret the slope and y-intercept.
y = 5x + 60
Slope: Test scores improve by 5 pts every hour studied.
Y-intercept: The lowest score was 60 after studying 0 hours.
Define
1. Line of FIT
2. Line of BEST FIT
FIT:
A line that models an approximately linear relationship. It lies as close to as possible to SOME points.
BEST FIT:
A line that models an approximately linear relationship. It lies as close to as possible to ALL points.
Identify the parent function. Then, describe transformations.
f(x)=(5/3)x2 + 7
1. Quadratic
2. Vertical Stretch by 5/3, shift UP by 7
Write a function g whose graph represents the indicated transformations.
f(x) = x. Vertical shrink by 1/3 followed by translation 4 units down.
g(x)= 1/3x - 4
A given graph has points (8, 12) and (3,53). What is the slope?
m = -8.2
The ticket price (x) and the number of people attending (y) is modeled by the equation of the line of best fit.
y = -3.2x + 880.
Find how many people will attend the show if the ticket price is $15.
832 people will attend the show if the price is $15.
Given the following rule: af(x)
if a > __, the function has a _______ ________.
If ___< a < ___, the function has a _______ ______.
if a >1, the function has a vertical stretch.
If 0< a < 1, the function has a vertical shrink.
Identify the parent function. Then, describe transformations.
f(x)= - (x-1)2 - 1.5
1. Quadratic
2. Reflection across x-axis, shift RIGHT 1, shift DOWN 1.5
Describe the transformations of the following function.
f(x) = 1/3|x - 2| - 4
Vertical SHRINK by 1/3, shift RIGHT 2, shift DOWN 4
A graph shows the height of a tree (y, ft) vs the age of the tree (x, years). Using the given equation, explain the meaning of the slope.
y = 1.5x
The tree grows 1.5 feet every year.
The African elephant population is endangered. A study started in 2022 modeled the amount of elephants left in the wild with the following equation. x represents the years after 2022, and y represents the wild elephant population.
y = -6.5x + 1350.
Interpret the slope and y-intercept.
Slope: We lose 6.5 elephants every year.
Y-intercept: In 2022, there were only 1350 elephants in the wild.
Write down the name of all 6 parent functions using the letter trick.
Identify the parent function. Then, describe transformations.
f(x)= 4|- x +3| - 9
1. Absolute Value
2. Vertical Stretch by 4, reflection across y-axis, shift LEFT by 3, shift DOWN by 9
Describe the transformations of the following function.
f(x) = 0.235(- x + 1.5)2 + 0.88
Vertical SHRINK by 0.235, reflection over Y-AXIS, shift LEFT 1.5, shift UP 0.88
A graph shows the height of a tree (y, ft) vs the age of the tree (x, years). Using the given equation, estimate the height of a tree that is 50 years old.
y = 1.5x
75 ft
The African elephant population is endangered. A study started in 2022 modeled the amount of elephants left in the wild with the following equation. x represents the years after 2022, and y represents the wild elephant population.
y = -6.5x + 1350
Estimate the wild elephant population in 2030.
x = 8, y=1,298