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1. The equation of a line: Given these two points A = (2,5) and B = (6,-1)
a. Find the distance between A and B. State the answer in reduced radical form.
b. Determine the slope of the line through A and B.
c. Write the equation of the line determined by A and B in slope-intercept form as a function. (f(x) =
mx+b)
d. Write the equation of the inverse to the original function f −1 (x) ( show work)
e. Sketch the points, the original line, f(x), and the inverse function f −1 (x) on this coordinate
system. Label each one.
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2. A rational function: Given f (x) =
x −1
2x + 3
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a. Determine the domain of f(x)
€ (a,0) as an ordered pair.
b. State the x-intercept
c. State the y-intercept (0,b) as an ordered pair.
d. f(-3) =
e. What is the result when you divide f(x) by
x 2 −1
? Show your work
2x 2 + 3x
3. Exponential and Logarithmic functions and expressions.
1
a. log 3
b. €Solve for x: log 4 (x −1) = 2
=
81
4. Graphing Transformations: Given this graph of y = x use the shifting techniques to draw
each of the following:
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€
€
y= x
€
€
y = x −2
y=− x
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y = x+3
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5. The number line Determine the value of each letter (showing your work) and place the letter at
the correct position on the number line. Draw a dot and write the letter.
S = (-8)2/3 =
2+
A=
1
4
H=
3
−27
0
0
0
€ T= π
1
−1
2
----|----|----|----|----|----|----|----|----|----|----|----|----|---|----|----|----|----|----|---€
-1
0
1
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M=
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Z=
6. Write And Solve An Equation. Five less than three times a number is six more than double the
number.
a. Write an equation for this sentence.
b. Solve the equation.
7. The Quadratic Formula Use the quadratic formula to determine the solutions to this equation:
f(x)=0. State answer in reduced radical form.
a. f(x) = 3x2 +6x -1
b. State the x-intercepts as ordered pairs.
c. State the y-intercept as an ordered pair.
d. Put in standard form: f (x)⋅ (x 2 +1) =
State Degree of part d:
Leading Coefficient:
8. Exponents and Radical Expressions: Simplify each expression as instructed.
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a. Simplify with positive rational exponents (no radicals)
x3 • 3 x6 =
⎛ 5x −2 y 7 ⎞ −2
b. State with positive exponents ⎜
3 −3 ⎟ =
⎝10x y ⎠
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9. A Polynomial Equation : Solve this equation. Note that it has been partially factored already.
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x2(x+1) –4(x+1) =
10. Radical Equation: Solve for x and check your answers.
11. System of equations
a.
Write a linear equation for each of these sentences, b. then solve the system.
• The first family entered the event with 3 adults and 2 children, paying
$17.00
• The second family entered with 4 adults and 6 children, paying $31.