Functions: domain and range

Question 1out of 10

Which condition is required for a table or mapping to define a function?

Only positive values may appear

One input x has two different outputs

Every output must equal its input

Each input x has exactly one output y

Question 2out of 10

Given f(x) = 5x + (-4), find x when f(x) = -14.

-2

-7

-9

Question 3out of 10

What is the range of f(x) = x²?

(−∞; 0]

(0; +∞)

[0; +∞)

Question 4out of 10

What exactly does the domain of a function mean?

It is only the set of outputs

The domain is the set of allowed input values

It is the number of graph points

It is always all real numbers

Question 5out of 10

Given f(x) = 2x + (-1), find f(4).

The notation f(x) represents the function value obtained for a particular value of x.

Substitute the given number for every x.
Perform the multiplication first.
Then add the constant term.

If x or the constant term is negative, use brackets during substitution so that its sign is preserved.

Question 6out of 10

Given f(x) = 4x + (-6), find x when f(x) = -10.

-8

-1

-3

Question 7out of 10

Give the domain of f(x) = 1/(x − (5)).

x ≠ 5

x = 5

All real numbers

[5; +∞)

Question 8out of 10

On which interval is f(x) = (x − (-4))(x − 8) negative?

(−∞; -4) ∪ (8; +∞)

(-4; 8)

[-4; 8]

Question 9out of 10

Find where f(x) = 5x + (25) crosses the x-axis.

(-10, -5)

(-5, 0)

(7, -1)

(-6, -2)

(-6, 1)

A graph crosses the x-axis where its y-coordinate equals zero.

For y = ax + b, substitute y = 0 and solve:

ax + b = 0, so x = −b/a.

The intersection point is written as (x, 0). Check the answer by substituting the calculated x into the original function.

Question 10out of 10

Find where f(x) = 8x + (-40) crosses the x-axis.

(-1, 5)

(11, 0)

(5, 0)

(4, -1)

(5, 3)

A graph crosses the x-axis where its y-coordinate equals zero.

For y = ax + b, substitute y = 0 and solve:

ax + b = 0, so x = −b/a.

The intersection point is written as (x, 0). Check the answer by substituting the calculated x into the original function.

Time left: 00:00:00

Finish the test

Functions: domain and range

The domain is the set of permitted input values x, while the range is the set of output values y attained by the function. On a graph, read the domain horizontally and the range vertically.

Finding restrictions

A denominator cannot be zero, and the radicand of an even root must be non-negative. Include an interval endpoint only when the function is defined there. An open or closed point on a graph also indicates whether a boundary value belongs to the set.

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