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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 1
Chapter 3, Problem 1

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=x2? What is its domain?
Nine coordinate plane graphs labeled A to I showing various functions, including a parabola opening upward at E.

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1
Identify the function given: ƒ(x) = x^2 is a quadratic function, which graphs as a parabola opening upwards.
Recall the shape of the graph of ƒ(x) = x^2: it is a U-shaped curve with its vertex at the origin (0,0).
Look at the provided basic graphs and select the one that matches this U-shaped parabola with vertex at the origin.
Determine the domain of ƒ(x) = x^2: since you can input any real number for x and get a real output, the domain is all real numbers.
Express the domain in interval notation as \((-\infty, \infty)\), meaning x can be any real number.

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Key Concepts

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

Quadratic Functions

A quadratic function is a polynomial function of degree two, typically written as f(x) = x². Its graph is a parabola that opens upwards, symmetric about the y-axis, with the vertex at the origin (0,0). Recognizing this shape helps identify the graph of f(x) = x².
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Solving Quadratic Equations Using The Quadratic Formula

Graph Interpretation

Graph interpretation involves analyzing the shape, position, and key features of a graph to match it with a given function. For f(x) = x², the graph is a U-shaped curve, and understanding these visual cues is essential to correctly identify the function's graph.
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Graphs and Coordinates - Example

Domain of a Function

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For f(x) = x², the domain is all real numbers since any real number can be squared without restriction.
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Related Practice
Textbook Question

Fill in the blank(s) to correctly complete each sentence. The circle with equation x2+y2=49x^2+y^2=49 has center with coordinates________ and radius equal to__________ .

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Textbook Question

Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1ƒ(x)=x+1 and g(x)=x2g(x)=x^2

(ƒ+g)(2) (ƒ+g)(2)

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Textbook Question

Fill in the blank to correctly complete each sentence. The point (4,_____ ) lies on the graph of the equation y = 3x - 6.

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Textbook Question

Fill in the blank(s) to correctly complete each sentence. The domain of the relation { (3,5), (4, 9), (10, 13) } is _____.

Textbook Question

Fill in the blank(s) to correctly complete each sentence. The graph of the line y= -2x+7 has slope ______ and y-intercept ______.

Textbook Question

Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them. P(3, -1), Q(-4, 5)

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