3. Find the zero of each of the following linear functions b) g(x)-45-x)-20x-6)+

Question

3. Find the zero of each of the following linear functions b) g(x)-45-x)-20x-6)+9 4. For each of the following equations, determine algebraically whether the graph of each equation is symmetric with respect to the x-axis, the y-axis, and the orngin. b) 8x +3-y 5. Alice invested a total of $6000, part at 3% simple interest and part at 4% simple interest. At the end of 2 years, the investments earned $416 interest. How much was invested at each rate? Show all your work. 6. Determine algebraically whether each of the following functions is even, odd, or neither even nor odd. Show all your work a) f(x)4x +6x b) g(x)=-9/ +3r-11 c) h(x)- -15 f(x)+f(-x) 7. Show that if fis any function, then the function E defined by E(x) s even.

Explanation / Answer

3. a) f(x) = 6-3x/5 = 0 if 3x/5 = 6 or x = 6*5/3 or, x = 10. Thus x = 10 is a zero of f(x).

b) g(x) = 4(5-x)-2(x-6)+9 = 20-4x -2x+12+9 = 41-6x. Now, 41-6x = 0 if 6x = 41 or, x = 41/6.Thus x = 41/6 is a zero of g(x).

4. a) 9y = 7x4- 8x . The function changes when we replace x by –x or y by –y. Thus, the given function is not symmetric about either X, or Y-Axis or the origin.

b) 8x6 +3 = y4. The function remains unchanged when we replace x $ by –x or y by –y. Thus, the given function is symmetric about both the X, Y-Axis and the origin.

c) 5x = |y|. The function remains unchanged when we replace y by –y, but changes when we replace x by –x. Thus, the given function is symmetric about only the X-Axis.

5. Let the amount invested at 3 % simple interest be $ x. Then, the amount invested at 4 % simple interest is $ (6000-x). Now, interest on $ x @ 3 % for 2 years is x *3/100 * 2 = 3x/50. Also, interest on $(6000- x) @ 4 % for 2 years is (6000-x)*4/100 *2 = 2(6000-x)/25. Since the total interest earned in 2 years is $ 416, hence 3x/50 +2(6000-x)/25 = 416 or, [3x+ 4(6000-x)]/50 = 416 or, 3x+ 4(6000-x) = 416*50 = 20800 or, 3x+24000-4x = 20800 or, x = 24000-20800 = 3200. Then 6000-x = 5000-3200 = 2800. Thus, $ 3200 are invested at 3 % and $ 2800 are invested at 4 %.

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