Question

Построить график функции у =(х-1)(3-х)

Answer 1

(3-х) • (х-1)=0 ←→ х=1, х=3
х=0, f(x)=–3

Answer 2

Graph of the Function y = (x-1)(3-x)

To graph the function y = (x-1)(3-x), we can start by finding the x and y-intercepts, determining the behavior of the function, and then plotting the graph.

1. Finding x-intercepts and y-intercepts: - To find the x-intercepts, set y = 0 and solve for x. - To find the y-intercept, set x = 0 and solve for y.

The x-intercepts and y-intercepts can help us understand the behavior of the function and where it crosses the x and y-axes.

2. Determining the behavior of the function: - We can analyze the behavior of the function by examining the signs of the factors (x-1) and (3-x) in different intervals of x.

3. Plotting the graph: - Using the information from the x and y-intercepts and the behavior of the function, we can plot the graph of y = (x-1)(3-x).

Let's proceed with the calculations and graphing.

Finding x-intercepts and y-intercepts:

To find the x-intercepts, we set y = 0 and solve for x: 0 = (x-1)(3-x)

To find the y-intercept, we set x = 0 and solve for y: y = (0-1)(3-0)

Determining the behavior of the function:

We can analyze the behavior of the function by examining the signs of the factors (x-1) and (3-x) in different intervals of x.

Plotting the graph:

Using the information from the x and y-intercepts and the behavior of the function, we can plot the graph of y = (x-1)(3-x).

Let's proceed with the calculations and graphing.