University:
University of Vermont
Course:
MATH 1034 | Pre-Calculus Mathematics
Academic year:

2024
Views:

304

Pages:

2
Author:

gydraddolmxla

PAL Worksheet 3 1. Give the domain of each function. Use interval notation: a. f (x) = 2x + 1 . 3x − 6 x2 − x − 11 2x2 − 3x − 9 √ c. h(x) = 8 − 3x p d. j(x) = 3 − |x| r −7 e. k(x) = 2x + 1 b. g(x) = f. l(x) = 3x2 − √ 4 x−1− 5 x−5 4x + 3 . 2x − 1 a. Is 9 in the domain of f ? Is 9 in the range of f ? Explain. 2. Let f (x) = b. Is 2 in the domain of f ? Is 2 in the range of f ? Explain. 1 1 c. Is in the domain of f ? Is in the range of f ? Explain. 2 2 3. Do the points (3, −8), (12, 4), and ( 32 , −10) lie on a line? If so, write the equation of the line in the form y = mx + b. If not, explain why not. Do the same for the points (1, −5), (7, 13) and (−2, −15). 4. Find the equation of each line described. Write your answers in the form y = mx + b. a. The line containing the points (−2, 7) and ( 12 , −2). b. The line with x-intercept 10 and y-intercept 8. c. The line with x-intercept 12 and slope 32 . d. The line with y-intercept 12 and slope 32 . e. The line containing the point (10, 3) and parallel to the line whose equation is 3x − 5y = 15. f. The line containing the point (10, 3) and perpendicular to the line whose equation is 3x − 5y = 15. 5. The graphs of various functions are shown. Determine whether the functions are even, odd, or neither. 6 40 4 20 2 -4 -3 -2 1 -1 2 3 4 -4 2 -2 4 -2 -20 -4 -40 -6 8 15 6 10 5 -4 4 2 -2 4 2 -5 -3 -10 -2 1 -1 -15 2 3 -2 5 4 4 2 3 2 5 -5 1 -2 -4 -4 2 -2 4 -1 6. Use algebraic techniques (checking to see if f (−x) = f (x) or f (−x) = −f (x)) to determine whether the given function is even, odd, or neither. a. f (x) = |x| √ b. f (x) = x 1 − x2 c. f (x) = x(x2 + 1) + x3 d. f (x) = |x| − x2 e. f (x) = x3 − 3 x2 + 1