Precalc - Review for test on 10-16-2015

Composite Functions with Integers

100

If f(x)=x+2 and g(x)=2x, this is f(g(3)).

What is 8

200

If f(x)=x+2 and g(x)=2x, this is g(f(-3))

What is -2

300

If f(x)=x^2+3 and g(x)=3x-1, then this is (f ° g)(5).

What is 199

400

If f(x)=x+1, g(x)=x^2, and h(x)=sqrt(x), then find f(g(h(16))).

What is 17

500

If f(x)=-x^2+2x and g(x)=x-2, what is (g ° f)(2)

What is -2

Composite Functions with Variables

100

If f(x)=2x+1, this is f(a-2)

What is 2a-3

200

If f(x)=3x^2 and g(x)=x-3, then find (f ° g)(x)

What is 3x^2-18x+27

300

If f(x)=3x^2 and g(x)=x-3, then this is (g ° f)(x)

What is 3x^2-3

400

let h(x)=x^2+1, then find h(x-2)

What is x^2-4x+5

500

If g(x)=x^2+7 and f(x)=x-3, find f(g(x))

What is x^2+4

Derivatives

100

The derivative of y = 3x² - 4

What is dy/dx = 6x

200

The first derivative of f(x) = -6x² + 10x - 14.

What is f'(x) = -12x + 10

300

The first derivative of y = sqrt(x)

What is y' = 1/ (2sqrt(x) )

400

The second derivative of 

y = 6x^4 - 1/2 x^2 - 10

What is 

y' = 72x^2 - 1

500

The equation of the tangent line to y = 2x³ - 6 at x=2 using the formula y-y₁=m(x-x₁) where (x₁,y₁) is a point and m is the slope

What is y - 10 = 24(x-2)

slogans

100

"Just do it"

Nike

200

The happiest place on earth

Disney

300

America runs on...

Dunkin

400

Think different

Apple

500

Taste the rainbow

Skittles

Simplifying Radicals

100

Rationalize the denominator.

sqrt(y)/sqrt(5)

sqrt(5y)/5

200

Rationalize the denominator.

sqrt(x/(8y))

sqrt(2xy)/(4y)

300

sqrt(8xy^2)/sqrt(2x^2)

(2ysqrt(x))/x

400

3/(2+sqrt(6)

(-6+3sqrt(6))/2

500

(3-sqrt(10))/(sqrt(5)-sqrt(2)

<p class="mathy">(sqrt(5)-2sqrt(2))/3</p>