How do you make a table and graph for h(x)=x34? What is the domain, range, and intercepts?

1 Answer
Feb 22, 2018

Table: See below.
Graph: See below.
Domain: All real numbers.
Range: All real numbers.
X-intercept: 3,4 (the cube root of 4) or about 1.59
Y-intercept: 4

Explanation:

1. Table
Here's a table for h(x)=x34, but only for 5x5:
|x | h(x)|
|5 | 129|
|4|68|
|3|31|
|2|12|
|1|5|
|0|4|
|1|3|
|2|4|
|3|23|
|4|60|
|5|121|

2. Graph
Here's the graph:
graph{x^3-4 [-16.02, 16.02, -11.43, 4.59]}

3. Domain
The domain is all the values of x that don't make the equation undefined. This is usually all real numbers, but if you have a fraction with x in the denominator or a radical with x inside it, it is not. Neither of these are true, so the domain is all real numbers.

4. Range
The range is all possible y-values. A cube root can be negative (such as 23=8), so the range is also all real numbers.

5. Intercepts
The y-intercept is 4, as the table above shows. The x-intercept is more complicated. Let's set h(x) (=x34) to zero and solve:
x34=0
Add 4 to both sides:
x3=4
Take the cube root of both sides:
x=3,4
x1.59
Our x-intercept is 3,4 or about 1.59.