Math example
- 1. SUMS AND DIFFERENCES OF FUNCTIONS Example:
- 2. Find each function sum, and graph the sum function. a) f(x)= x2, g(x)= 2 b) f(x)= x2, g(x)= 3x 1.a) Let h(x) equal the sum of f(x) and g(x) h(x)= f(x) + g(x) h(x)= x2 + 2
- 3. To get the coordinates for h(x), add the y-points together. At -3, 2+9 = 11 Therefore (-3,11) At -2, 2+2 = 4 Therefore (-2,4) At -1, 2+1 = 3 Therefore (-1,3) At 0, 0+2 = 2 Therefore (0,2) At 1, 1+2 = 3 Therefore (1,3) At 2, 2+2 = 4 Therefore (2,4) At 3, 2+9 = 11 Therefore (3,11)
- 4. b) f(x)= x2, g(x)= 3x Let p(x) equal the sum of f(x) and g(x). p(x)= f(x) + g(x) p(x)= x2 + 3x
- 5. To get the coordinates for p(x), add the y-points. At -3, 9+(-9) = 0 Therefore (-3,) At -2, 4+(-6) = -2 Therefore (-2,-2) At -1, 1+(-3) = -2 Therefore (-1,-2) At 0, 0+0 = 0 Therefore (0,0) At 1, 1+3 = 4 Therefore (1,4) At 2, 4+6 = 10 Therefore (2,10)
- 6. To find domain and range, you have to find the midpoint. Midpoint: p(x)= x2 + 3x Factor p(x)= x(x+3) x=0 x+3=0 x= -3 Therefore x = 0, -3
- 7. To find the midpoint, add the x-intercepts and divide by 2. Midpoint = 0 + (-3) 2 = -3 2 Substitute this value into the formula to find the y coordinate. p(-3/2) = (-3/2)2 + 3(-3/2) = -9/4
- 8. Therefore D= {XER} R= {YER, y > -9/4}