Functions

1. Determine whether each of the following equation defines \( y \) as a function of \(x\).  solution

(a) \( y = -x^2+5x-7 \)   (b)  \( x^2-y^2 = 9\)   (c)  \( x = 8|y| \)   (d) \( xy=-1\)

2.  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) \( f(-x) \)

3.  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) \(\displaystyle{ f(x)= \frac{\sqrt{4-2x}}{x+5}}\)

4.  Let \( f(x) = 3x^2-x-2 \).      solution

(a) Is \( (-1,0) \) a point of the graph of \( f \)?

(b) Find all \( x \) such that \( (x, 2) \) is on the graph of \( f \).

(c) Find all \( x \)-intercepts of the graph of \( f \).

(d) Find all \( y \)-intercepts of the graph of \( f \).