Section 1.1 Homework

 

1.  If

$$\begin{gathered} f\left(x\right) = \frac{x^2–9x}{x–9} and g\left(x\right) = x \\ Is it true that f=g \end{gathered}$$

 

A. Yes

B. No.

 

 

2.  The graph of a function f is given.

(a) State the value of f(1).
(b) Estimate the value of f(−1).
(c) For what values of x is f(x) = 1?
 x=
(d) Estimate the value of x such that f(x) = 0.
x = 
(e) State the domain and range of f. (Enter your answers in interval notation.)
domain         

range    
    
(f) On what interval is f increasing? (Enter your answer using interval notation.)

 

3. The graphs of f and g are given.

(a) State the values of f(−4) and g(−2).

f(−4) =

g(−2) =

(b) For what values of x is f(x) = g(x)? (Enter your answers as a comma-separated list.)
x = 

(c) Estimate the solutions of the equation f(x) = −1. (Enter your answers as a comma-separated list.)
x = 

(d) On what interval is f decreasing? (Enter your answer using interval notation.)

(e) State the domain and range of f. (Enter your answers in interval notation.)
domain        

range

(f) State the domain and range of g. (Enter your answers in interval notation.)
domain        

range    

 

4. Consider the following graph.

 

Determine whether the curve is the graph of a function of x.

A. Yes, it is a function.
B. No, it is not a function.    

If it is, state the domain and range of the function. (Enter your answers in interval notation. If the curve is not the graph of a function of x, enter DNE.)
domain        

range    

 

5.  Consider the following graph.

Determine whether the curve is the graph of a function of x.

A. Yes, it is a function.
B.  No, it is not a function.    

If it is, state the domain and range of the function. (Enter your answers using interval notation. If it is not a function, enter DNE in all blanks.)
domain    

range

 

 

6.   Consider the following graph.

Determine whether the curve is the graph of a function of x.

A. Yes, it is a function.
B. No, it is not a function.    

If it is, state the domain and range of the function. (Enter your answers using interval notation. If it is not a function, enter DNE in all blanks.)

domain    
    
range    

 

 

7  If

$f\left(x\right) = 4x^2–x+5, find the following$

f(2) =  

f(−2)

f(a) =    

f(−a) =    

f(a + 1) =    

2f(a) =    

f(2a) =    

f(a2) =    

[f(a)]2 =    

f(a + h) =    

 

8.   A spherical balloon with radius r inches has volume 

$V\left(r\right) = \frac{4}{3}\pi r^3$

.   Find an expression that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r + 3 inches. (Express your answer in terms of 𝜋 and r.)

 

9.  Evaluate the difference quotient for the given function. Simplify your answer.

$f\left(x\right) = 5 + 2x –x^2, \frac{f(3+h)–f\left(3\right)}{h}$

10.   Find the domain of the function. (Enter your answer using interval notation.)

$f\left(x\right) = \frac{x+4}{x^2–49}$

 

11.  Find the domain of the function. (Enter your answer in interval notation.)

$h\left(x\right) = \frac{1}{\sqrt[4]{x^2 –3x}}$

 

12.  Find the domain and range of the function. (Enter your answers using interval notation.)

$h\left(x\right) = \sqrt{64 – x^2}$

 

domain    
    
range    

 

13.  Evaluate f(−4), f(0),  and f(3)  for the piecewise defined function.

$f\left(x\right) = \left\{\begin{array}{l}x+3 if x < 0\\ 1–x if x \ge 0\end{array}\right.$

f(−4)     = 

f(0)     = 

f(3)     =     

 

 

14.  Sketch the graph of the function.

f(x) = 4x + 4|x|

 

15. Sketch the graph of the function.

$f\left(x\right) = \left\{\begin{array}{l}2 \left|x\right| if \left|x\right| \le 1\\ 2 if \left|x\right| > 1\end{array}\right.$