Sec 2.1: Functions

1. Evaluate the function \( f(x) = x^2-7x+8\) at the given values of the independent variable and simplify.   solution

(a) \( f(-2) \)    (b) \( f(x+1) \)   (c) \( f(-x) \)

2.  Find the domain of the following functions in interval notation.   solution

(a)   \( \displaystyle{f(x)=\frac{3}{x+2}} \)  (b)   \(\displaystyle{f(x)=\frac{x^2+9}{x^2-9}}\)  (c)  \(\displaystyle{f(x)=x^2-x+1}\)   (d) \( \displaystyle{ f(x)= \frac{2}{\sqrt{4-x^2}} }\) (e)   \(\displaystyle{ f(x)= \frac{\sqrt{4-2x}}{x+5}}\)

3. Evaluate the difference quotient as indicated.

(a) \( \dfrac{f(a+h)-f(a)}{h}\)   for   \( f(x)=x^2\)  solution

(b) \( \dfrac{f(4+h)-f(4)}{h}\)   for   \( f(x)=\sqrt{x}\)  solution

(c) \( \dfrac{f(x+h)-f(x)}{h}\)   for   \( f(x)=\dfrac{1}{\sqrt{x}}\)  solution

4. Given \( f(x)=5x-7 \). Evaluate \(\dfrac{f(1+h)-f(1)}{h} \).  solution

5. Find the difference quotient \(\dfrac{f(4+h)-f(4)}{h} \) and simplify for the function \( f(x)=\sqrt{x}\).   solution

6. Find the difference quotient \(\dfrac{f(a+h)-f(a)}{h}\) and simplify for the function \(f(x)=3x^2-5x \).  solution