Welcome to MA 107 Pre-Requisite Skills Review!

Functions

100

Find the domain of the function using interval notation: 5x/(x-10).

(-infinity, 10) U (10, infinity)

200

Find the real-valued roots of the quadratic function: y=x²+2x-1.

x= -1 + sqrt(2), 

x= -1 - sqrt(2)

300

Consider g(x)=2x. Find g(g(x)).

g(g(x))=4x

400

Simplify: x²(x⁵)+(x³)³+3(x+6)+5(x+2)²+2^x(2²)

x⁹+x⁷+5x²+23x+38+2^x+2

500

Consider the function f(x)=(1+.04/x)¹²+2(x-5)²-(3-x)²-6x²-3. Evaluate f(-2) and approximate to 2 decimal places.

46.83

Solving for a Variable

100

Solve for y: 2y-6=9

y=7.5

200

Solve for x: 3x^2+3x-6=0

x=-2 and x=1

300

a) Does (x-7)²=-9 have a real-valued solution?

b) Solve for r: r²=49

a) No! We cannot take the square root of a negative number and get a real number.

b) r=7 and r=-7

400

Solve the inequality: -2x+8>0

x<4

500

Simplify: (x²/2)/(9x/3).

x/6

Hodgepodge

100

Graph a constant function. Label your axes, scale, and the equation of the function.

Answers vary but will be a horizontal line and will have the form y=c.

200

Graph the function y=x^2. Then, find the x and y intercepts of the function.

Will be a parabola and the x and y intercepts are both 0.

300

Draw a 170 degree angle.

Will be in second quadrant, 10 degrees above of the x-axis (which is 180 degrees).

400

What is the domain of y=ln(x)?

(0,infinity)

500

Solve e⁶=10. Approximate to 2 decimal places.

.38