grade 10 question

Define a relation in mathematics.

• A relation is a function that maps one set to another.

• A relation is a set of ordered pairs that defines a relationship between elements of two sets.

• A relation is a collection of unordered elements.

• A relation is a single element in a set.

What is the difference between a relation and a function?

• A relation must have one output for each input, while a function can have multiple outputs.

• A relation is always a subset of a function, and functions cannot be relations.

• A relation can have multiple outputs for a single input, while a function has exactly one output for each input.

• All relations are functions, but not all functions are relations.

Give an example of a function and explain why it is a function.

• f(x) = 2x + 3

• f(x) = 3x - 4x^2

• f(x) = x^2 - 5

• f(x) = sin(x) + 1

What is the domain of a function?

• The set of all possible input values for a function.

• The range of a function.

• The slope of a function.

• The output values of a function.

What is the range of a function?

• The set of all possible input values of a function.

• The set of all possible output values of a function.

• The difference between the highest and lowest output values.

• The average of all output values of a function.

How can you determine if a relation is a function using the vertical line test?

• A relation is a function if it has at least one vertical line that intersects the graph.

• A relation is a function if every horizontal line intersects the graph at least once.

• A relation is a function if no vertical line intersects the graph more than once.

• A relation is a function if it is represented by a straight line on a graph.

What is a one-to-one function? Give an example.

• f(x) = x^2, where each input x produces the same output for different inputs.

• An example of a one-to-one function is f(x) = 2x, where each input x produces a unique output.

• f(x) = sin(x), which is not a one-to-one function due to periodicity.

• f(x) = 3x + 1, which can produce the same output for different inputs.

Explain what an inverse function is.

• An inverse function is a function that adds to the output of another function.

• An inverse function is a function that reverses the effect of another function.

• An inverse function is a function that only applies to positive numbers.

• An inverse function is a function that multiplies the input by a constant.

What is a composite function? Provide an example.

• An example of a composite function is (f ∘ g)(x) = f(g(x)), where f(x) = x + 2 and g(x) = 3x. Thus, (f ∘ g)(x) = f(3x) = 3x + 2.

• A composite function is simply the sum of two functions, like f(x) + g(x).

• An example of a composite function is f(g(x)) = x^2 + 3.

• A composite function is defined as f(x) * g(x), where f(x) = 2x and g(x) = x - 1.

How do you find the inverse of a function algebraically?

• Replace f(x) with y, swap x and y, solve for y, and replace y with f⁻¹(x).

• Graph the function and reflect it over the line y=x.

• Set y equal to x, then solve for x and replace x with f⁻¹(y).

• Differentiate the function and then integrate to find the inverse.