Precalclus Section 1.5 Part 2

Precalclus Section 1.5

Combinations of Functions

Multiple Choice

$$f\left(x\right)\ =\ \sqrt[]{x-4}$$ and $$g\left(x\right)\ =\ x^2+4$$   

Find : $$f\left(x\right)\ +\ g\left(x\right)$$  

• $$\sqrt[]{x-4}+x^2+4$$  

• x

• $$\sqrt[]{x}+x^2$$  

• $$\sqrt[]{x-4}-x^2-4$$  

Multiple Choice

$$f\left(x\right)\ =\ \sqrt[]{x-4}$$ and $$g\left(x\right)\ =\ x^2+4$$   

Find : $$f\left(x\right)\ -\ g\left(x\right)$$  

• $$\sqrt[]{x-4}-x^2+4$$  

• x

• $$\sqrt[]{x}+x^2$$  

• $$\sqrt[]{x-4}-x^2-4$$  

Multiple Choice

$$f\left(x\right)\ =\ \sqrt[]{x-4}$$ and $$g\left(x\right)\ =\ x^2+4$$   

Find : $$f\left(x\right)\ \div\ g\left(x\right)$$  

• $$\frac{\sqrt[]{x-4}}{x^2+4}$$  

• $$x$$

• $$\sqrt[]{x}+x^2$$  

• $$\frac{\left(x^2-4\right)}{\sqrt[]{x-4}}$$  

Multiple Choice

$$f\left(x\right)\ =\ \sqrt[]{x-4}$$ and $$g\left(x\right)\ =\ x^2+4$$   

Find : $$\left(f\ \circ\ g\right)\left(x\right)\$$  

• $$\sqrt[]{x^2+x}$$  

• x

• $$\sqrt[]{x}+x^2$$  

• $$x+2$$  

• $$\sqrt[]{x-4}\left(x^2+4\right)$$  

Multiple Choice

$$f\left(x\right)\ =\ \sqrt[]{x-4}$$ and $$g\left(x\right)\ =\ x^2+4$$   

Find : $$\left(g\ \circ\ f\right)\left(x\right)\$$  

• $$\sqrt[]{x^2+x}$$  

• x

• $$\sqrt[]{x}+x^2$$  

• $$x+2$$  

Open Ended

This is a potential problem area on quizzes and tests

Explain the difference between the two notations.

Multiple Choice

If $$g(x)=3x+4$$ and $$h(x)=3x-1$$

$$find\ \ \ g(h(x))=?$$

• $$-9x+11$$

• $$9x^2+9x-4$$

• $$9x+1$$

• $$9x+11$$

Multiple Choice

If $$p(x)=4x-5$$ and $$q(x)=2x^2$$

$$Find\ \ p(q(x))$$

• 8x² + 5
• 8x² - 10x
• 8x² - 5
• $$32x^2-80x+50$$

• None of these

Fill in the Blanks

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

Multiple Choice

If $$f\left(x\right)=2x$$   and  $$g\left(x\right)=2x^2-1$$   find $$g\left(f\left(x\right)\right)$$  

• $$4x^2-1$$  

• $$4x^3-2x$$  

• $$8x^2-1$$  

• $$16x^2-1$$  

Multiple Choice

If $$f\left(x\right)=x^2+6$$   and $$g\left(x\right)=2x-4$$  , find $$f\left(g\left(x\right)\right)$$  

• $$2x^2-12x-4$$  

• $$2x^2+12x-4$$  

• $$4x^2-16x+22$$  

• $$x^3-2x^2+1$$  

Multiple Choice

f(x) = 2x - 5

g(x) = -4x - 2

Find f(g(-2))

• 25

• -25

• -7

• 7

​The Petri Dish problem

​So, basically you have a petri dish in a refrigerator and you are going to take it out and the temperature is going to rise as a result.

​

​Based on the rising temperature the bacteria will grow more quickly.

​

​You will have 2 minutes to find the composite function.

Math Response

Find the composition

N(T(t)) = ?

Type answer here

Correct Answer: 320t^2+420

Deg^°

Rad

Multiple Choice

Using the $$N(T(t))\ =\ 320t^2+420$$  

Find N(2) = ?

• 1060

• 1700

• 860

• none of these

Fill in the Blanks

Using the $N(T(t))\ =\ 320t^2+420$  

When will the count reach 2000?

answer to the nearest tenth

Math Response

Evaluate $$f\left(g\left(-6\right)\right)\$$

Type answer here

Correct Answer: -1

Deg^°

Rad

​Homework

​Page 56 - 58


# 7, 10, 13, 17, 21, 25, 32, 33, 37, 42, 45, 49, 57, 62, 67, 69, 71

​Homework

​Page 56 - 58

​#10, 13, 28, 32, 33, 37, 42, 44, 45, 49, 57, 62