Mac1105C Test 1 Review

Lines

100

1.Find the equation of the line perpendicular to

y = (-5/3) x -7, through (1,3).

y = (5/3)x + 4/3

200

Daily Double: 

solve: log₃x+log₃(x-2) = 1

3

300

The population of Quincy has shown linear increase from 2004-2014.  In 2004, the population of Quincy was 6,885.  By 2014 it had risen to 7,955.

Find a linear equation P as a function of t, the number of years since 2004

P(t) = 107t+6885

400

If you have a line of y = -7x + 20. What would the slope of a line parallel to that be?

m = -7

500

If the population is growing according to this equation, P(t) = 107t+6885, and it has been measured since 2004. When would the population reach 9000?

In 20 years or 2024

Circles

100

Find the midpoint between points (4, -5) and (3, 2)

(7/2, -3/2)

200

Find the distance between points (4, -5) and (3, 2).

distance = sqrt (50)

300

Find the radius of
(x -3)²+ (y+4)²=49

radius = 7

400

Determine the equation of the circle with radius 6 and whose center is (3, -1)

(x - 3)²+ (y + 1)² = 36

500

Find the center of
(x -3)²+ (y+4)²=49

(3, -4)

Absolute Value

100

Solve for x:  |2x -9|=3

(-oo, 3) U (6, oo)

200

Solve in interval notation:  |2x+3| ≥  7

(-oo, -5] U [2, oo)

300

Solve in interval notation:  |2x+3| < 7

(-5, 2)

400

Solve in interval notation: |2x+3| <  -7

DNE or no solution

500

|2x+3| > - 7

(-oo, oo) or all real numbers

Inequalities & polynomials & logs

100

Write log_b (m²2/n)as a sum or difference of logs (without powers):

2log_bm + log_b2 - log_bn

200

35)Solve for x:  5e^(x+2)=40

x = ln (8) - 2

300

40)Solve the equation for x by completing the square:x² - 6x=34

in the form (    )² = __

(x - 3)² = 43

400

Solve the quadratic equation:  x²+13=7x algebraically (in exact, radical form)

x = 7/2 +/- i sqrt(3) /2

500

Solve in interval notation:    x³ ≥ 4x² -3x

[0,1] U [3,oo)

Graphs

100

14)Find the axis of symmetry for f(x) = 3x²-5x+4

x = 5/6

200

How would you test if a graph is symmetric to the origin?

Reflect both around the x-axis and y-axis. if your original point is still on the graph, it is symmetric to the origin.

300

33)Determine the relative maxima and minima (if any) of:  f(x)= x⁵ -3x³

maxima (-1.342, 2.898)

minima: (1.342, -2.898)

400

Use g(x) = √(x   to answer the question: find the graph after it is shifted left 3 units, and then up 2.

g(x) = sqrt(x + 3) + 2

500

When graphing: g(x) = log₂(x+1), is there an asymptote? is there an x-intercept or y-intercept?

vertical asymptote: x = -1

intercept (0,0)