Functions
Solving for a Variable
Hodgepodge
100

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

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

100

Solve for y: 2y-6=9

y=7.5 (or y=15/2)

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

Simplify: (x2/2)/((9x)/3).

x/6

200

Solve for x: 3x2+3x-6=0

x=-2 and x=1

200

Graph the function y=x2. Then, find the x and y intercepts of the function.

Will be a parabola and the x and y intercept are both (0,0).

300

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

g(g(x))=4x

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

300

Draw a 170 degree angle.

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

400

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

x9+x7+5x2+23x+38+2x+2

400

Solve the inequality: -2x+8>0

x<4

400

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

(0,infinity)

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.

46.78

500

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

x= -1 + sqrt(2), x= -1 - sqrt(2)

500

Solve ex=10. Approximate to 2 decimal places.

2.30

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