For numbers 13, 16, a, b, c, f, and g, find a.) x-intercept, b.) y-intercept, c.) zeros of the function, d.) vertical asymptote, and e.) horizontal asymptote. Write the given, solution and answer in A4 sized bond paper, hand-written. Bring your output in portfolio on Monday, and get ready for boardwork. God bless.13. f(x) = 2x +3 5x + 7 x x² 15. f(x) = 2+13 7x3 17. h(x) = x³-3x² + 6x 10x5 + x + 31 19. g(x) = -6 3x7 + 5x² - 1 21. f(x) = 6x3 - 7x + 3 14. f(x) = 2x²³ +7 x^3 - x² + x + 7 7 16. f(x) = 3x + 2 x²-2 9x4 + x 2x + 5x2 - x + 6 18. h(x) = x² + 7x² - 2 20. g(x) = x² - x + 1 5x8 - 2x² + 9 22. h(x) = 3 + x - 4x³
Answer (1)
Answer:Problem 13: a. x-intercept-3/2b. y-intercept3/7c. Zeros of the functionx = -3/2d. Vertical asymptotex = -7/5e. Horizontal asymptotey = 2/5Explanation for Problem 13Assuming the function is ( f(x) = \frac{2x + 3}{5x + 7} ) (interpreting the garbled text as a rational function with numerator 2x +3 and denominator 5x +7; ignoring "x x²" as potential typing error).a. To find the x-intercept, set f(x) = 0: ( 2x + 3 = 0 ), so x = -3/2. Verify denominator ≠ 0: 5(-3/2) + 7 = -0.5 ≠ 0.b. To find the y-intercept, evaluate f(0) = 3/7.c. Zeros are where numerator = 0 and denominator ≠ 0, so x = -3/2 (same as x-intercept).d. Vertical asymptote where denominator = 0 and numerator ≠ 0: 5x + 7 = 0, x = -7/5 (numerator at x = -7/5 is 2(-7/5) + 3 = -14/5 + 15/5 = 1 ≠ 0).e. Horizontal asymptote: degrees of numerator and denominator are equal (both 1), so y = leading coefficient ratio 2/5.Problem 16: ( f(x) = \frac{3x + 2}{x^2 - 2} )a. x-intercept-2/3b. y-intercept-1c. Zeros of the functionx = -2/3d. Vertical asymptotex = \sqrt{2}, x = -\sqrt{2}e. Horizontal asymptotey = 0Explanation for Problem 16Assuming the function is ( f(x) = \frac{3x + 2}{x^2 - 2} ) (interpreting the initial terms as numerator and denominator; extra terms like "9x4 + x 2x +5x2 - x +6" ignored as potential typing error or separate problem).a. Set f(x) = 0: 3x + 2 = 0, x = -2/3. Verify denominator ≠ 0: (-2/3)^2 - 2 = 4/9 - 18/9 = -14/9 ≠ 0.b. f(0) = 2/-2 = -1.c. Zeros: x = -2/3 (same as x-intercept).d. Denominator = 0: x^2 - 2 = 0, x = \pm \sqrt{2}. Numerator at these points: 3(\sqrt{2}) + 2 ≠ 0, 3(-\sqrt{2}) + 2 ≠ 0.e. Degree of numerator (1) < degree of denominator (2), so y = 0.
