Short Answer 
A function maps each input from a domain to a single output in the range. To find the intercepts of the equation (y – 1 = frac{2}{3}(x – 3)), set (y = 0) to get the x-intercept at (x = frac{3}{2}) and (x = 0) to find the y-intercept at (y = -1), which can then be used to graph the function.
Step 1: Understand What a Function Is
A function is a mathematical concept that assigns each element from one set (called the domain) to a specific element in another set (called the range). In simpler terms, it takes an input and produces a single output. Think of it as a machine: you input a value, and it outputs another value systematically.
Step 2: Calculate Intercepts of the Given Function
To find the intercepts of the function represented by the equation y – 1 = (2/3)(x – 3), you’ll need to substitute specific values for x and y. Follow these steps to find both intercepts:
- X-intercept: Set y = 0 in the equation, solve for x, which gives x = 3/2.
- Y-intercept: Set x = 0 in the equation, solve for y, which results in y = -1.
Step 3: Identify the Graph Based on Intercepts
With the calculated intercepts, you can now graph the function. You should look for a graph that meets the following criteria:
- Intersects the x-axis at x = 3/2.
- Intersects the y-axis at y = -1.
These characteristics will help you identify the correct graph representing the equation y – 1 = (2/3)(x – 3).