In Saxon Algebra 1 Lesson 119, Grade 9 students learn to identify and compare linear, quadratic, and exponential function families by analyzing their parent functions, graphs, tables of values, and rates of change. The lesson covers key characteristics such as domain, range, and constant versus non-constant rates of change to distinguish among the three function types. Students practice matching equations like f(x) = 3^x or f(x) = x^2 - 1 to their correct function family using multiple representations.
Section 1
📘 Graphing and Comparing Linear, Quadratic, and Exponential Functions
A function family is a set of functions whose graphs have similar characteristics.
Next, you’ll learn to identify these families—linear, quadratic, and exponential—from graphs, tables, and real-world scenarios.
Section 2
Function Families
A function family is a set of functions whose graphs have similar characteristics, formed by transforming a parent function.
Think of a parent function like as the original superhero. Other functions in its family, like , have the same U-shape power but might be shifted up, down, or stretched. They all share a core identity!
is the parent of the quadratic family, which includes .
belongs to the linear family, whose parent is .
Section 3
Linear Functions
Parent Function: . These functions have a constant rate of change, and their graph is a straight line.
This is like earning an allowance! If you get five dollars every week, your savings grow at a steady, predictable rate. There are no surprises, just a straight line of cash piling up, which makes it easy to graph and predict.
The cost of gas at 3.25 dollars per gallon is a linear model because the rate is constant.
A data table shows a linear pattern if the difference in values is always the same for each step in .
Section 4
Quadratic Functions
Parent Function: . The graph is a parabola that changes direction at a maximum or minimum value called the vertex.
Picture throwing a ball! It flies up, reaches a peak height (the vertex), and then arches back down. That classic U-shaped path is the signature move of a quadratic function. It always has one turning point, which makes it unique.
The height of a thrown object over time is modeled by a quadratic function.
The graph of is a U-shaped parabola that opens upwards.
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Section 1
📘 Graphing and Comparing Linear, Quadratic, and Exponential Functions
A function family is a set of functions whose graphs have similar characteristics.
Next, you’ll learn to identify these families—linear, quadratic, and exponential—from graphs, tables, and real-world scenarios.
Section 2
Function Families
A function family is a set of functions whose graphs have similar characteristics, formed by transforming a parent function.
Think of a parent function like as the original superhero. Other functions in its family, like , have the same U-shape power but might be shifted up, down, or stretched. They all share a core identity!
is the parent of the quadratic family, which includes .
belongs to the linear family, whose parent is .
Section 3
Linear Functions
Parent Function: . These functions have a constant rate of change, and their graph is a straight line.
This is like earning an allowance! If you get five dollars every week, your savings grow at a steady, predictable rate. There are no surprises, just a straight line of cash piling up, which makes it easy to graph and predict.
The cost of gas at 3.25 dollars per gallon is a linear model because the rate is constant.
A data table shows a linear pattern if the difference in values is always the same for each step in .
Section 4
Quadratic Functions
Parent Function: . The graph is a parabola that changes direction at a maximum or minimum value called the vertex.
Picture throwing a ball! It flies up, reaches a peak height (the vertex), and then arches back down. That classic U-shaped path is the signature move of a quadratic function. It always has one turning point, which makes it unique.
The height of a thrown object over time is modeled by a quadratic function.
The graph of is a U-shaped parabola that opens upwards.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter