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Unformatted text preview: becomes 1 instead of 0.) Remember: In determining the graph of a function in the xyplane, 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 xyplane 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 xyplane, 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 xyplane 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 xaxis, 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 xyplane 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 gridin question. For quest...
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