College Algebra

please also give complete solution to each question. Its for Mth 103 class. It’s due tommorow nigh

Math 103 Unit 2 Homework
Work needs to be shown fully for all problems requiring it otherwise, no credit will be given.
1. Use the point slope formula to write an equation of the line having the given conditions. Write
the answer in slope intercept form (if possible). (5pts)
a. Passes through (-6,2) and (6,5)
b. Passes through (-3.2) and m= 0
c. Passes through (-4,-2) and is parallel to the line defined by 5x + y=-5
d. Passes through (-2, 3) and is perpendicular to the line defined by 5y = 2x.
e. Passes through (9, 12) and is parallel to the x axis.
2. If you are given a line whose with the given slope, determine the slope of a line parallel and
perpendicular to the given line, if possible. (2pts)
a. m = -1
parallel
Perpendicular
b. m = 24
parallel
Perpendicular
3. Determine if the lines defined by the given equations are parallel, perpendicular, or neither and
then explain why? (2pts)
a.
-8
y = X + 3
7
7
x
y=-x+8
8
b. 2x – 4y = 3
4x + 8y = 8
4. Describe the translations used to graph the given function. (2pts)
a. f(x) = VX – 3+1
Parent Function f(x) = Vx
b. f(x) = { 1x – 11 +2
Parent Function f(x) = |x|
a. Parent Function: y = x
5. Write a function based on the given parent function and transformations in the given order. 1pt
1.Shift 5.2 units to the left
2. Reflect across the y axis
3. Shift upwards 8.1 units
New Function
6. Determine whether the graph of the equation is symmetric with respect to the x axis, y axis,
origin, or none of these. All work must be shown for each test. ( 4 pts)
a. y=x4 – 3
b. x = ly| + y2
Test for y axis
Test for y axis
Test for x axis
Test for x axis
Test for origin
Test for origin
Symmetric with respect to
Symmetric with respect to
9. Evaluate the function for the given value of x. (3pts)
$(x)={*
-3x+ 5 xs-2
x2 +1
X>-2
a) f(-5) =
b) f(-2) =
c) f(0)
10. Refer to the function r, p, and q. Find the indicated functions and then write their domains in
interval notation. (2 pts)
r(x) = 5x
P(x) = x2 + 9x
9(x) = 79 – x
a. (r/p)(x)
Domain
b. (q/f)(x)
Domain
7. Determine if the function is even, odd, or neither. All work must be shown for each test (2pts)
b. g(x)= 14 – x?
a. f(x) = – 4×3 + x
Test for Y axis
Test for y axis
Test for Origin
Test for origin
Even, Odd, or Neither
Even, Odd, or Neither
8. Sketch the graph of the following piecewise function on the set of axes provided.
State three points used to graph each function. (3 pts)
09
f(x) =
–x? +2 x 51
Vx-1
f(2)={-131
4
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2
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-5
-4
-3
-2
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-1
0
1
2
3
4
5
6
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-2
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-3
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-4
-5
Function 1
Function 2