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Math 1021 Exam 3 Sample Problems
College Algebra (MATH 1021)
Louisiana State University of Alexandria
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Math 1021 Exam #3 Sample Problems
Determine the slope, y -intercept, and average rate of change of each linear function and sketch its graph.(a) f ( x ) = 3 x – 4 (b) g ( x ) = -(2/5) x + 7
Find the vertex and intercepts of the quadratic function f ( x ) = - x 2 – 4x + 5 and use them to sketch the graph of the function.
Find the vertex and intercepts of the quadratic function them to sketch the graph of the function. f ( x ) = 2 x 2 – 6 x and use
Determine whether each quadratic function has a minimum or maximum value and determine the minimum/maximum point.(a) f ( x ) = 3 x 2 + 15 x + 25 (b) g ( x ) = -0 x 2 + 16 x + 490
(a) Find a polynomial function having the zeros 5 (multiplicity 2), −7, and 7. (b) Find a polynomial function with real coefficients having the zeros 1 and 2 + i. For problems 6-8, solve each inequality and express the solution set in interval notation.
x 2 + x – 6 ≤ 0
2 x 3 > 8 x
(3 x + 8)/( x – 4)
Determine the following for the function f ( x ) = -4 x ( x + 3) 2 ( x – 2) 2. (a) The zeros of the function and their multiplicities.(b) Whether the graph of the function crosses or touches the x -axis at each zero. (c) The maximum number of turning points possible for the graph.(d) The power function that resembles the graph of at the ends.
For problems 10-12 find the domain and vertical, horizontal, and/or oblique asymptotes of each rational function.
10. f ( x ) = ( x – 3)/( x 2 – 7 x + 12)
11. f ( x ) = (3 x + 1)/( x + 4)
f ( x ) = (2 x 2 + 5 x + 3)/( x + 2)
Use the rational zeros theorem to find the real zeros of f ( x ) = 2 x 3 + x 2 – 13 x + 6.
Find the complex solutions of x 4 + 4 x 3 – x 2 + 16 x – 20 = 0.
If (a) ( f ( xf ) = ⸰ xg 2 )( + 5 and x ) g (b) (( x ) = 7 g ⸰ x – 1, find the following. f )( x )
If (a) ( f ( xf ) = √ ⸰ gx )(1) + 3 and (b) ( g ( x ) = 4/( g ⸰ xf )(6) + 1), find the following.
Find the inverse of each of the following functions.(a) f ( x ) = 3 x – 2 (b) g ( x ) = ( x – 3) 2 , x ≥ 3 (c) h ( x ) = 4/( x – 5)
Math 1021 Exam 3 Sample Problems
Course: College Algebra (MATH 1021)
University: Louisiana State University of Alexandria
