Name ______________________________________________
Date __________________________________
Thurgood Marshall Academy Public Charter High School – Pre-Calculus
Notes #15 – Function Notation and Equations
Topic: General Properties of Functions
Objectives:

15.1 Answer questions about functions whose equations are given using function notation.
Standards:

F-IF.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to
each element of the domain exactly one element of the range. If f is a function and x is an element of its domain,
then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

F-IF.2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use
function notation in terms of a context.
Key concepts:

function notation
A.
Recall: 𝑓(3) = 7 means the ordered pair ___________ satisfies the function named _____.
B.
Suppose f is the function whose ordered pairs satisfy 𝑦 = 2𝑥 + 1.
Complete:
𝑓(5) =
𝑓(4) =
𝑓(3) =
In general, 𝑓(𝑥) =
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C.
Suppose g is the function whose ordered pairs satisfy 𝑦 = 3𝑥 + 5.
Complete:
𝑔(6) =
𝑔(7) =
𝑔(8) =
In general, 𝑔(𝑥) =
D.
Integrate!
When the ordered pairs of a function f satisfy 𝑦 = 2𝑥 + 1, then 𝑓(𝑥) =_____________________.
When the ordered pairs of a function g satisfy 𝑦 = 3𝑥 + 5, then 𝑔(𝑥) =_____________________.
Generalize:
E.
In the rest of this lesson, we will answer questions that we’ve already learned how to answer, except now the
equations will be written using ______________________________________.
You can answer these questions by replacing _______ with ______.
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F.
Suppose 𝑓(𝑥) = 3𝑥 − 8. Find x such that 𝑓(𝑥) = −5.
G.
Generate three solutions of 𝑓(𝑥) = 𝑥 2 + 3𝑥 + 1.
H.
Suppose that 𝑔(𝑥) = |𝑥 − 10|. Find 𝑔(3).
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I.
Find all intercepts of 𝑔(𝑥) = −3𝑥 + 12.
J.
Sketch 𝑓(𝑥) = 𝑥 3 . Show the coordinates of five ordered pairs on your sketch.
K.
Describe the end behavior of 𝑝(𝑥) = 𝑥 10.
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Practice Exercises #15 – Function Notation and Equations
15.1 Answer questions about functions whose equations are given using function notation.
1.
Suppose 𝑓(𝑥) = 2𝑥 − 12. What is 𝑓(−3)?
2.
Generate any four solutions of 𝑓(𝑥) = (𝑥 + 2)(𝑥 − 3).
3.
Suppose that 𝑔(𝑥) = 5 − 9𝑥. Find x such that 𝑔(𝑥) = −13.
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4.
Find all intercepts of 𝑔(𝑥) = √𝑥 + 9.
5.
Sketch 𝑓(𝑥) = 𝑥 2 . Show the coordinates of five ordered pairs on your sketch.
6.
Describe the end behavior of 𝑚(𝑥) = 𝑥 11.
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7.
Suppose 𝑓(𝑥) = (𝑥 − 8)(𝑥 − 2). Find x such that 𝑓(𝑥) = 0.
8.
Generate three solutions of 𝑛(𝑥) = 2𝑥 + 1.
9.
Suppose that 𝑔(𝑥) = −𝑥 2 − 5𝑥. Find 𝑔(−1).
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10.
Find all intercepts of 𝑔(𝑥) = (𝑥 + 3)(𝑥 − 2).
11.
Sketch 𝑓(𝑥) = 𝑥 5 . Show the coordinates of five ordered pairs on your sketch.
12.
Describe the end behavior of 𝑝(𝑥) = 𝑥 30.
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