Let denote any one of the functions graphed in the British insigniz or the f sergeant’s insignia. Compare and and and If is a f(1) f(–1), f(2.5) f(–2.5), f(3.7) f(–3.7). x sergeant’s number such that 0 7, how do and compare? x f(x) f(– x) Let be a constant other than the number 0 and let denote the function whose formula a g is given by = You studied the shapes of these graphs in Unit 1. Look back at g(x) ax2. some examples for particular choices of What type of symmetry do these graphs have? a. If is a positive number, how do and compare? x g(x) g(– x) We call a function an even function if, for any number in the domain of is also in f x f, x – the domain and = f(– x) f(x). Suppose is an even function and the point (3, 5) is on the graph of What other point f f. do you know must be on the graph of Explain. f? Suppose is an even function and the point (– 2, 4) is on the graph of What other point f f. do you know must be on the graph of Explain. f? If (a, is a point on the graph of an even function what other point is also on the graph b) f, of f? What symmetry does the graph of an even function have? Explain why. Consider the function which is an even function. Part of the graph of is shown to k, k the right. Using the information that is an even function, complete the graph for the k rest of the domain.
Let f denote any one of the functions graphed in the British sergeant’s insigniz or the sergeant’s insignia. Compare f(1) and f(–1), f(2.5) and f(–2.5), f(3.7) and f(–3.7). If x is a number such that 0 x 7, how do f(x) and f(– x) compare? Let a be a constant other than the number 0 and let g denote the function whose formula is given by g(x) = ax2. You studied the shapes of these graphs in Unit 1. Look back at some examples for particular choices of a. What type of symmetry do these graphs have? If x is a positive number, how do g(x) and g(– x) compare? We call a function f an even function if, for any number x in the domain of f, – x is also in the domain and f(– x) = f(x). Suppose f is an even function and the point (3, 5) is on the graph of f. What other point do you know must be on the graph of f? Explain. Suppose f is an even function and the point (– 2, 4) is on the graph of f. What other point do you know must be on the graph of f? Explain. If (a, b) is a point on the graph of an even function f, what other point is also on the graph of f? What symmetry does the graph of an even function have? Explain why. Consider the function k, which is an even function. Part of the graph of k is shown to the right. Using the information that k is an even function, complete the graph for the rest of the domain.
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