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Unformatted text preview: becomes 1 instead of 0.) Remember: In determining the graph of a function in the xy-plane, use y to signify f(x) and, conversely, use x to signify f(y). Example: If f(x) = x + 3, then the line shown in the xy-plane above is the graph of (A) f(x) (B) f(x – 6) (C) f(x + 6) (D) f(x + 3) (E) f(x – 3) Solution: The correct answer is (E). The figure shows the graph of the function f(x) = x (or y = x). To determine which of the five answer choices transforms the original function f(x) = x + 3 to the function f(x) = x, substitute the variable expression in each choice, in turn, for x in the original function. Choice (E) is the only one that provides an expression that achieves this transformation:
f ( x − 3) = ( x − 3) + 3 f ( x − 3) = x y=x To help you determine the effect of a function’s transformation on the function’s graph, you can tabulate some (x,y) pairs based on the new function, plot the points on the xy-plane, and then connect them. www.petersons.com Additional Geometry Topics, Data Analysis, and Probability 289 Example: If f(x) = x2, then the graph shown in the xy-plane above best represents which of the following functions? (A) f(–x) (B) f(x – 1) (C) f(x + 1) (D) f(x2 + 1) (E) f(x2 – 1) Solution: The correct answer is (B). The figure shows the graph of y = x2, but translated to the right. Substitute the variable expression given in each answer choice, in turn, for x in the function f(x) = x2. Performing this task for choice (B) yields the equation f(x) = (x – 1)2, or y = (x – 1)2. Identify and plot some (x,y) pairs. (Since the vertex in the graph lies along the x-axis, let x = 0 in order to establish the vertex’s coordinates.) Here are some (x,y) pairs for the equation y = (x – 1)2 : (0,1)(1,0), (2,1), (3,4), (–1,4) Plotting these points in the xy-plane reveals a graph whose key features match those of the figure provided in the question. www.petersons.com 290 Chapter 16 Exercise 4
Work out each problem. Question 1 is a grid-in question. For quest...
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- Spring '10