College Algebra SI - Fridays

Functions and Graphs

100

Identify whether the following relation is a function and explain why: the set of ordered pairs {(1,2), (2,3), (1,4)}.

no. fails vertical line test. 1 maps to 2 unique outputs.

200

Describe the transformations (shifts, reflections, stretches/compressions) that map the parent function f(x)=|x| to g(x) = -2|x+3| + 4 and state the vertex of g(x).

shift up 4

shift left 3

stretch by 2

reflect across x axis

vertex: (-3,4)

300

Given f(x)=3x-7, find the inverse function f^-1(x) and state its domain and range.

x=3y-7

get back in terms of y=x

y=(x+7)/3

400

Find the x- and y-intercepts of the function 

f(x)=(x²−4) / (x−1) 

and describe any holes or vertical asymptotes.

x int: 2, -2

y int: 4

no holes

vertical asymptote: 1

500

Determine the domain, range, intercepts, and end-behavior of f(x)=sqrt(5−2x).

Domain (-inf,5/2]
Range [0,inf)
y int: sqrt(5) ~ 2.236
x int: 5/2
End Behavior:
As x->-inf, y->inf
As x->2.5, y->0
the graph terminates at the x intercept.

Linear Equations & Linear Inequalities

100

solve for x:

3x-7=11

x=6

200

Solve -3(2x-1)>= 9

x<=-1

300

A line passes through the points (1,4) and (5,−2). Find its equation in slope-intercept form.

m=y₁-y / x₁-x

y=-3/2x+11/2

400

Solve the compound inequality: 2≤3x+1<11.

1/3≤x<10/3
[1/3,10/3)
[0.33,3.33)

500

 Solve the inequality (2x−3) / (x+4) ≤ 1

-4<x≤7

we dont know if x+4 is positive or negative, so you cant multiply both sides by it since the inequality would have to flip if its negative. 

Systems of Linear Equations

100

Solve the system:

x+y=5

x-y=1

x=3, y=2

200

Solve the system:

2x+3y = 12

y=4-x

x=0

y=4

300

Solve the system

3x-2y=7

6x-4y=14

(infinitely many solutions)

y = (3/2)x - (7/2)

400

solve the system:

x+y=5
y+z=10

x+z=7

x=1

y=4

z=6

500

solve the system:

x+2y-z=3

2x-y+3z=1

-x+y+2z=4

x=0
y=2
z=1

Matrix Addition / Subtraction

100

Compute:

1	2
3	4

+

0	2
−1	5

1	4
2	9

200

Compute

12	7
3	15

+

8	2
6	−4

20	9
9	11

300

Subtract:

5	7	0
−1	2	3

−

2	4	−1
0	2	1

3	3	1
−1	0	2

400

If A =

2	−1
0	3

and B =

a	b
c	d

, find B such that A + B =

5	0
0	7

B =

3	1
0	4

500

10	0	−3
4	−1	2
6	5	8

−

4	−2	5
1	3	−6
−2	7	4

6	2	−8
3	−4	8
8	−2	4

Matrix Multiplication / Division

100

Compute

3

2	−1
0	4

6	−3
0	12

200

3-part question. Answer ALL correctly

A) How many rows and columns does a matrix of M × N dimensions have?

B) Matrix A is M × N and Matrix B is P × N. Are these compatible for multiplication?

C) In this matrix, what is the value of element a₂₁?

7	3
−5	0

A) rows: M, Columns: N

B) No.

C) -5

300

Compute

1

2

3

4

11

400

compute

1	0
2	3

4	1
0	−2

4	1
8	−4

500

Compute if possible to do:

1	0	2
−1	3	1

3	1
2	−2
0	4

3	9
3	−3