NAME:
PRE-CALCULUS
PRACTICE
SEMESTER TEST
Simplify each exponential expression.
(-9x y) (-2x y )
3
1.
6 4
Add or subtract terms whenever possible.
3
2.
24xy3 - y 3 81x
Use the graph to determine…
3. Function’s Domain
Function’s Range
X-intercepts
Y-intercepts
Missing function values, indicated by question marks, below the graph
Represent the volume of each figure as a polynomial in standard form.
4.
Factor completely.
4
3
2
5. 6x -18x +12x
Find and simplify the difference quotient for the given function.
6.
f ( x + h) - f ( x)
,h¹ 0
h
f(x) = - 3x2 + 2x – 1
Use the given conditions to write an equation for each line in point-slope
form and slope-intercept form.
7. Passing through (3 , 5) and (8 , 15)
Find f + g , f – g , f g , f . Determine the domain for each function.
g
8.
f ( x) = 5- x
2
g( x) = x2 + 4x-12
Evaluate the indicated function using the following
f ( x) = 2x- 5
b) g( x) = 4x-1
a)
c) h( x) = x2 + x+ 2
9. f -1( h(3) )
Divide using long division. State the quotient, q(x), and the remainder,
r(x).
10. (18𝑥 4 + 9𝑥 3 + 3𝑥 2 ) ÷ (3𝑥 2 + 1)
List all the possible rational roots. Use synthetic division to test the
possible roots and find an actual root. Then use the quotient to find the
remaining roots.
11. 𝑥 3 − 2𝑥 2 − 7𝑥 − 4 = 0
Graph the following rational function.
12.
𝑥 2 −6𝑥+9
𝑥−9
Convert each equation to standard form by completing the square on x.
Find the vertex, x-intercepts and y-intercepts, if possible. Finally, graph
the parabola.
13. 𝑥 2 − 4𝑥 + 𝑦 − 5 = 0