Even, Odd and Domain of a Function

1.  A point \((-4,7)\) is on the graph.

(a) If \(f(x)\) is an odd function, list another point that must also be on the graph.

(b) If \(f(x)\) is an even function, list another point that must also be on the graph.

2. Determine algebraically whether each of the following equations is even, odd, or neither. solution

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

3. Find the average rate of change of the function as \( x \) changes from \(a\) to \(b\). solution

       \(f(x)=2x^3-1;      a =  -4,  b = 1\) 

4.  Find the average rate of change of the function \( f(x) = 5x^2-2x+7 \) as \( x \) changes from \(-2\) to \(3\). solution

5.  Find and simplify the difference quotient for the function \( f(x)=x^2-5x\) answering the following. solution

(a) Find \(f(x+h)\)            (b)  Find \(f(x+h)-f(x) \)             (c) Find \(\displaystyle{\frac{f(x+h)-f(x)}{h}} \)

6. The graph of the function is given below. Use the graph to find each of the following. solution

(a) The domain and range of the function           (b) The intercepts, if any     

(c) The intervals on which the function is increasing, is decreasing, or is constant

(d) Whether the function is even, odd, or neither