Characteristics of Graphs Review

Characteristics of Graphs Review

Read each question carefully and provide detailed answers, showing all work where applicable.

1. Consider the function f(x) = √(x - 3).

a) Determine the domain of f(x).

b) Determine the range of f(x).

2. Which of the following functions has both an x-intercept at (2,0) and y-intercept at (0,-4)?

3. Which type of symmetry does the function y = x³ exhibit?

4. For the function f(x) = -2x⁴ + 3x² - 1, as x → ∞, f(x) →  , and as x → -∞, f(x) →  .

5. The end behavior of a rational function is determined by the   of the numerator and denominator.

6. Analyze the characteristics of the graph shown below.

a) Domain:  

b) Range:  

c) x-intercept(s):  

d) y-intercept(s):  

e) Intervals where the function is increasing:  

f) Intervals where the function is decreasing:  

g) Relative maximum(s) (if any):  

h) Relative minimum(s) (if any):  

i) End behavior as x → ∞:  

j) End behavior as x → -∞:  

7. A function can have more than one y-intercept.

8. An even function is symmetric with respect to the y-axis.