Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

0. Review of College Algebra

Functions

Trigonometry

0. Review of College Algebra

Functions

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1:02 minutes

Problem 53

Textbook Question

Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6.ƒ(p)

Verified step by step guidance

Identify the function f(x) which is given as f(x) = -3x + 4.

To find f(p), substitute x with p in the function f(x).

Replace x with p in the expression: f(p) = -3(p) + 4.

Simplify the expression by performing the multiplication: -3p.

Combine the terms to get the simplified expression for f(p).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Evaluation

Function evaluation involves substituting a specific value into a function to determine its output. For example, if you have a function f(x) and you want to find f(p), you replace x with p in the expression of f. This process is fundamental in understanding how functions behave at different points.

Linear Functions

A linear function is a polynomial function of degree one, typically expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept. In the given function f(x) = -3x + 4, the slope is -3, indicating a decrease in value as x increases. Understanding linear functions is crucial for analyzing their graphs and behaviors.

Quadratic Functions

Quadratic functions are polynomial functions of degree two, represented as g(x) = ax² + bx + c. The function g(x) = -x² + 4x + 1 is a downward-opening parabola due to the negative leading coefficient. Recognizing the characteristics of quadratic functions, such as their vertex and axis of symmetry, is essential for solving related problems.