Calculus Jeopardy

Define

100

What is a real zero of a function?

When f(x) = 0

200

What type of function is (x²+2x+1)/x?

A Rational Function

300

What is the degree of f(x) = x(x-1)²?

3

400

What is the range of a function?

The y values that have at least one corresponding x value on the function.

500

If a function is 1-1, what does that mean?

Every input results in a unique output.

Solve

100

f(x) = 2x²+12x+16 = 0

x = ?

x = -4 or x = -2

200

f(x) = 2^x-5, g(x) = x²+x-2

f(g(3)) = ?

f(g(x)) = 32

300

What is the domain of (x³+2)/(x²-4)?

x = (-inf, -2), (-2, 2), (2, inf)

400

cos(a) = 3/5

sin(a) = ?

sin(a) = 4/5

500

3|2x+4| - 7 = 1

x = ?

x = -2/3 and x = -10/3

Find Mistakes

100

A polynomial is factored:

2x²+6x-20 = 2(x²+3x-10) = 2(x+2)(x+5)

Is this correct? Why or why not?

The last step should be:

= 2(x-2)(x+5)

200

This is not a function: y²+x²=1

Is this statement correct? Why or why not?

It is correct.

300

sin(2x) is a sin curve stretched vertically by a factor of 2.

Is this correct? Why or why not?

It is stretched horizontally.

400

(3+2i)(7-4i) = 21-4i+141-8i² = 29+10i

Is this incorrect? If so, what is wrong?

It is correct

500

A function is reduced as follows:

(x²+6x-30)/(x²-16) = (x+4)(x+2)/(x+4)(x-4) =

(x+2)/(x-4)

Is there anything wrong with this? If so, what?

The domain (x can not equal -4) needs to be noted.