MATH 1150
Practice Test 1
Last Name:
First Name:
√
15−3x
x+8 .
f (x) = x10x
2 +1
Problem 1. Find the domain of f (x) =
Problem 2. The graph of the function
is shown below.
C
A
B
(a) Is f even or odd?
(b) Find the coordinates of the points B and C, assuming that the x-coordinate of B is −1.
(c) Solve the equation f (x) = x to find the coordinate of the point A.
(d) Does f have an inverse?
Problem 3. Sketch the graph of the function.
(a) y = −|x + 2| + 3
(b) y = 21 (x − 2)2 + 1
Problem 4. Find the formula for the inverse of the function f (x) =
x
3−x .
Problem 5. Write an equation for the parabola with vertex ⟨−2, 5⟩ and containing the point ⟨0, 9⟩.
Problem 6. Sketch the graph of the function
f (x) = 3x3 − 15x2 + 18x
by (a) applying the Leading Coefficient Test, (b) finding the real zeros of the polynomial, (c)
plotting sufficient solution points, and (d) drawing a continuous curve through the points.
Problem 7. Find the remaining factors of the polynomial
2x3 + 11x2 − 21x − 90,
given that (x + 6) is one of its factors.
Problem 8. Completely factor the polynomial using complex numbers
f (x) = 2x4 − 2x3 + 16x − 16
(begin by applying the Rational Zero Test).