Graphs for Precalculus:: Function Families and Transformations Flashcards (43 Cards) — Study Online

Curriculum Overview

Learn functions by reading their graphs. 43 flashcards, each with a real graph on the front: the parent functions, shifts, reflections and stretches (parent graph in blue, transformed graph in red), domain and range from a graph, even and odd functions, inverse functions, polynomial zeros and end behavior, and sine, cosine, tangent, exponential and logarithm graphs. Every answer is checked and explained. For precalculus, college algebra, SAT/ACT math and the start of calculus.

Topics & Key Concepts

precalculus algebra parent functions transformations graph shifts reflections stretches domain and range even and odd inverse functions polynomial zeros end behavior sine cosine tangent exponential logarithm SAT ACT college algebra

Sample Flashcard Questions & Answers

Showing 8 of 43 cards

Question #1 Active Recall

The graph of a parent function is shown. Name it and give its domain, its range and its symmetry.

Answer & Explanation:

**\(y=x\)**, the identity (linear) function.

Domain: all real numbers. Range: all real numbers. It is **odd** (symmetric about the origin) and passes through \((0,0)\) and \((1,1)\); the slope is 1.

Question #2 Active Recall

The graph of a parent function is shown. Name it and give its domain, its range and its symmetry.

Answer & Explanation:

**\(y=x^2\)**, the quadratic (squaring) function, a parabola.

Domain: all real numbers. Range: \([0, \infty)\). It is **even** (symmetric about the y-axis). The vertex (lowest point) is \((0,0)\); it passes through \((\pm 1, 1)\) and \((\pm 2, 4)\).

Question #3 Active Recall

The graph of a parent function is shown. Name it and give its domain, its range and its symmetry.

Answer & Explanation:

**\(y=x^3\)**, the cubic function.

Domain: all real numbers. Range: all real numbers. It is **odd** (symmetric about the origin), always increasing, and flat for an instant at the origin (an inflection point). It passes through \((1,1)\) and \((2,8)\).

Question #4 Active Recall

The graph of a parent function is shown. Name it and give its domain, its range and its symmetry.

Answer & Explanation:

**\(y=|x|\)**, the absolute value function.

Domain: all real numbers. Range: \([0, \infty)\). It is **even** (symmetric about the y-axis). The graph is a V with its vertex at \((0,0)\) and slopes \(-1\) and \(1\).

Question #5 Active Recall

The graph of a parent function is shown. Name it and give its domain and its range.

Answer & Explanation:

**\(y=\sqrt{x}\)**, the square root function.

Domain: \([0, \infty)\) (no square roots of negative numbers). Range: \([0, \infty)\). It starts at \((0,0)\), passes through \((1,1)\), \((4,2)\) and \((9,3)\), and rises ever more slowly. It is neither even nor odd.

Question #6 Active Recall

The graph of a parent function is shown. Name it, give its domain, its range, its symmetry and its asymptotes.

Answer & Explanation:

**\(y=\dfrac{1}{x}\)**, the reciprocal function.

Domain: all real numbers except 0. Range: all real numbers except 0. It is **odd** (symmetric about the origin). The vertical asymptote is \(x=0\) and the horizontal asymptote is \(y=0\). It passes through \((1,1)\) and \((-1,-1)\).

Question #7 Active Recall

The graph of a parent function is shown. Name it, give its domain, its range and its horizontal asymptote, and name the point where it crosses the y-axis.

Answer & Explanation:

**\(y=e^x\)**, the natural exponential function.

Domain: all real numbers. Range: \((0, \infty)\) (always positive). The horizontal asymptote is \(y=0\) on the left (the graph gets close to the x-axis but never touches it). It crosses the y-axis at \((0,1)\) and always increases.

Question #8 Active Recall

The graph of a parent function is shown. Name it, give its domain, its range and its vertical asymptote, and name the point where it crosses the x-axis.

Answer & Explanation:

**\(y=\ln x\)**, the natural logarithm.

Domain: \((0, \infty)\). Range: all real numbers. The vertical asymptote is \(x=0\) (the graph drops without bound as \(x \to 0^+\)). It crosses the x-axis at \((1,0)\) and always increases, slowly. It is the inverse of \(y=e^x\).

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