Inequalities/Matrices
1.When graphing an inequality, if the inequality is > or <, draw a ______ line to show that the points on the line are not part of the solution. (fill the blank)
answer: doted line
1. Which of following is slope-intercept form?
A. y=mx+b
B. Ax+By = c
C. y= Ax2+C
answer: A
B is called standard form
1. Which of the following is a quadratic function?
A. y = 2x3+x+1
B. y = 2x+1
C. y = 2x2 +x+1
answer: C
the form of quadratic function is y =ax2+bx+c
Which of following is exponential function?
A. f(x)=x2
B. f(x)=2x
C. f(x)=(x+5)3
B. f(x)=2x
The exponential function is f(X)=bx where b is a number such that b >0 and b not equal to 1.
2. if we have -3 < x < 10, which of the following listed x values satisfy the inequality
A. -3, 4, 5, 6, 8
B. -1, 5, 8, 9, 0.5
C. 0, 2, 6, 10, 7
answer: B
2. What is the formula to find the slope m if you are given two points?
answer: m = (y2-y1)/(x2-x1)
2. If f(x) = ax2+bx+c, what is x coordinate for the vertex point?
answer: -b/2a
2. What is the answer for log2(8)?
the answer is 3. log2(23)=3
3. Which of the following is the identity matrix?
A. 1 1 1 B. 0 1 1
1 1 1 1 0 1
1 1 1 1 1 0
C. 1 0 0
0 1 0
0 0 1
answer: C
3. The linear function y = mx +b , what is m? what is b?
Answer: m is slope, b is y-intercept
3. Given a quadratic function f(x)=-2x2+3x+5. Does the graph of this function open up or open down? why?
answer: open down, because a = -2 < 0 which opens down.
3.Which of the following is true?
A. loge(x) = ln(x)
B. log10(x) = ln(x)
C. log5(x) = ln(x)
4. What is the solution for the following matrix?
1 1 | 5
0 0 | 1
answer: there are no solutions
because the second row 0 does not equal to 1
4. If you need to find x-intercept of a linear function y = 2x-2, what do you do?
A. set x=0, solve for y
B. set y=0, solve for x
C. set both x and y = 0
answer: B
A is to find y-intercept
4. See the graph, what is the range of this graph?
answer: [-5, infinity)
4. What is the domain of following function?
f(x) = log5(-2x - 1)
Answer: x < -1/2
-2x-1 > 0 (add 1 on both sides)
-2x > 1 (divide -2 on both sides, divide negative needs to flip the inequality)
x < -1/2
5. See following two matrices
2 4 -2 -1.5 8 3/2
A= 3 -1 2.4 B= 12 1 4
5 1 0 -5 -7.1 -3
Which of the following statement is true?
a. A22 > B21
b. A31 < B11
c. A11 < B23
answer: c is correct
A11=2, B23=4, 2< 4
5. What does the graph look like for a linear function?
answer: a straight line
5. Given a cost function p(x) = 2x+3, what is the revenue function R(x)?
answer: R(x) = 2x2+3x. R(x) = x*p(x) = x(2x+3)
5.What is the equivalent way of writing the following function?
y = logax
answer: x = ay