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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1:56 minutes

Problem 47

Textbook Question

Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6.g(-2)

Verified step by step guidance

Substitute \(-2\) into the function \(g(x)\).

The function \(g(x)\) is given by \(g(x) = -x^2 + 4x + 1\).

Replace \(x\) with \(-2\) in the expression: \(g(-2) = -(-2)^2 + 4(-2) + 1\).

Calculate \(-(-2)^2\): First, square \(-2\) to get \(4\), then multiply by \(-1\) to get \(-4\).

Calculate \(4(-2)\) to get \(-8\), then add \(-4\), \(-8\), and \(1\) together.

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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 input value into a function to determine its output. For example, to find g(-2), you replace x in the function g(x) with -2, allowing you to compute the corresponding value of the function.

Quadratic Functions

A quadratic function is a polynomial function of degree two, typically expressed in the form g(x) = ax² + bx + c. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the leading coefficient (a).

Simplification of Expressions

Simplification involves reducing an expression to its simplest form, making it easier to understand or compute. This can include combining like terms, factoring, or performing arithmetic operations to arrive at a more concise expression.