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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 51
Chapter 3, Problem 51

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. y=x2

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Identify the given equation: \(y = x^2\). This is a quadratic function where \(y\) is the square of \(x\).
Choose at least three values for \(x\). For example, select \(x = -1\), \(x = 0\), and \(x = 2\) to find corresponding \(y\) values.
Calculate the \(y\) values by substituting each chosen \(x\) into the equation \(y = x^2\). For instance, when \(x = -1\), compute \(y = (-1)^2\).
Create a table of ordered pairs \((x, y)\) using the values found. For example, the pairs might look like \((-1, 1)\), \((0, 0)\), and \((2, 4)\).
To graph the equation, plot each ordered pair on the coordinate plane and connect the points with a smooth curve forming a parabola opening upwards.

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Key Concepts

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

Ordered Pairs as Solutions to Equations

An ordered pair (x, y) represents a solution to an equation if substituting x into the equation yields the corresponding y value. For example, in y = x², if x = 2, then y = 4, so (2, 4) is a solution. Creating a table of such pairs helps visualize the relationship between variables.
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Equations with Two Variables

Quadratic Functions and Their Graphs

A quadratic function has the form y = ax² + bx + c, where the graph is a parabola. For y = x², the parabola opens upward with its vertex at the origin (0,0). Understanding this shape helps in sketching the graph accurately based on the ordered pairs.
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Graphs of Logarithmic Functions

Plotting Points and Graphing Equations

Graphing involves plotting ordered pairs on the coordinate plane and connecting them smoothly. For y = x², plotting points like (-1,1), (0,0), and (1,1) reveals the curve's shape. This visual representation aids in understanding the function's behavior.
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Related Practice
Textbook Question

Find the value of the function for the given value of x.

f(x)={3if 0<x≤410−2[[5−x]]if x>4, for , for x=6.2f(x)=\(\begin{cases}\)3 & \(\text{if }\)0<x\(\leq\)4\\ 10-2[\(\left\]\lbrack\)5-x]\(\right\[\rbrack\) & \(\text{if }\)x>4,\(\text{ for }\]\end{cases}\),\(\text{ for }\)x=6.2

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Textbook Question

Find the value of the function for the given value of x.

f(x)={5if 0<x≤220−3[[2−4x]]if x>2 , for x=5.6f(x)=\(\begin{cases}\)5 & \(\text{if }\)0<x\(\leq\)2\\ 20-3[\(\left\]\lbrack\)2-4x]\(\right\[\rbrack\) & \(\text{if }\)x>2\(\text{ }\]\end{cases}\),\(\text{ for }\)x=5.6

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Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=x2

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Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. ƒ(0)

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For each line, (a) find the slope and (b) sketch the graph. y = 2x - 4

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Textbook Question

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (-1, 4), parallel to x+3y=5

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