Understanding Linear Functions and Graphs

The video tutorial explains how to find the range of a linear function with a restricted domain. It begins by introducing the problem and the importance of understanding domain restrictions. The instructor then demonstrates how to sketch the graph of the function, highlighting the gradient and y-intercept. The process of determining the range is explained by substituting values into the function and identifying the highest and lowest y-values. The tutorial emphasizes the importance of using correct brackets to represent the range accurately. Finally, the instructor provides tips for solving similar problems, noting common student difficulties and the simplicity of the linear function involved.

What is the function f(x) given in the problem?

• f(x) = x - 10

• f(x) = 10 + x

• f(x) = 10 - x

• f(x) = x + 10

Why is it important to sketch the graph of the function?

• To calculate the slope

• To find the domain

• To determine the range

• To identify the x-intercept

What is the first step in finding the range of the function?

• Calculate the slope

• Sketch the graph

• Find the x-intercepts

• Determine the domain

What is the gradient of the function f(x) = 10 - x?

• -1

• 10

• 1

• 0

What is the y-intercept of the function f(x) = 10 - x?

• 0

• 10

• 1

• -10

How do you determine the range of the function from the graph?

• By finding the x-intercepts

• By looking at the domain

• By calculating the slope

• By identifying the highest and lowest y-values

What does an open circle on the graph indicate?

• The value is the maximum

• The value is the minimum

• The value is included in the range

• The value is not included in the range

What does a closed circle on the graph indicate?

• The value is included in the range

• The value is the minimum

• The value is not included in the range

• The value is the maximum

What is the range of the function f(x) = 10 - x if a < b?

• (10 - a, 10 - b]

• [10 - b, 10 - a)

• [10 - a, 10 - b)

• (10 - b, 10 - a]

Why is the highest value not included in the range?

• Because of the closed circle

• Because of the open circle

• Because it is the maximum value

• Because it is the minimum value