Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

3. Functions

Intro to Functions & Their Graphs

College Algebra

3. Functions

Intro to Functions & Their Graphs

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1:34 minutes

Problem 79

Textbook Question

An equation that defines y as a function of x is given. (b) Find ƒ(3). y+2x^2=3-x

Verified step by step guidance

Identify the function ƒ(x) from the given equation. Start by isolating y on one side of the equation. In this case, from the equation y + 2x^2 = 3 - x, solve for y to express it as a function of x: y = 3 - x - 2x^2.

Substitute x = 3 into the function ƒ(x) to find ƒ(3). Replace every x in the function expression with 3: ƒ(3) = 3 - 3 - 2(3)^2.

Simplify the expression inside the function. First, calculate the square of 3, then multiply it by 2, and finally perform the subtraction as indicated: ƒ(3) = 3 - 3 - 2(9).

Continue simplifying by performing the arithmetic operations: ƒ(3) = 3 - 3 - 18.

Combine all the constants to find the value of ƒ(3): ƒ(3) = -18.

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Key Concepts

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

Functions

A function is a relation that assigns exactly one output (y) for each input (x). In this context, the equation y + 2x² = 3 - x defines y as a function of x, meaning for every value of x, there is a corresponding value of y. Understanding functions is crucial for evaluating specific inputs, such as ƒ(3).

Solving Equations

Solving equations involves manipulating the equation to isolate the variable of interest. In this case, we need to rearrange the equation y + 2x² = 3 - x to express y in terms of x. This process is essential for finding the value of the function at a specific point, such as when x equals 3.

Substitution

Substitution is the process of replacing a variable in an expression or equation with a specific value. To find ƒ(3), we substitute x with 3 in the rearranged equation. This step is vital for calculating the output of the function at that particular input.