Functions and Their Properties

The video tutorial explains the subtraction of functions, focusing on transforming subtraction into addition for easier problem-solving. It begins by identifying f(x) and g(x) on a graph, then demonstrates how to convert the subtraction of functions into an addition problem. The tutorial guides viewers through graphing the difference of functions and concludes with verifying the results using algebraic methods.

What is the x-intercept of the function f(x) as described in the video?

• 1

• 0

• 2

• -1

How is the gradient of f(x) described in the video?

• 1

• 2

• 3

• 4

What is the key idea behind converting subtraction of functions into addition?

• Multiplying the functions

• Adding the opposite of the function being subtracted

• Adding the same function

• Subtracting the same function

What is the equivalent expression for '10 take away 3' as explained in the video?

• 10 minus 3

• 10 minus negative 3

• 10 plus 3

• 10 plus negative 3

What is the y-value at the x-intercept of -2 for the function f(x) - g(x)?

• 5

• -2

• -5

• 0

What happens when you add two straight lines together?

• You get another straight line

• You get a parabola

• You get a curve

• You get a circle

What is the gradient of the resulting graph of f(x) - g(x)?

• 2

• 3

• 1

• 0

What is the y-intercept of the graph of f(x) - g(x) as verified algebraically?

• -1

• -2

• -3

• -4

What is the purpose of using algebra to check the graph?

• To calculate the area under the graph

• To verify the graph matches the expected outcome

• To determine the slope of the tangent

• To find the x-intercepts

What is the final expression for f(x) - g(x) as derived in the video?

• x - 3

• 2x - 3

• 2x + 3

• x + 3