Question

Select all that apply.

A) the domain is the set of all real numbers

B) f(-2)=1

C) The domain is {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}

D) f(5)=1

E) This is not a function

F) f(-1)=0

G) f(5)=4

H) This is a function

I) The range is the set of all real numbers

J) The range is 4 and all real numbers less than or equal to 2

L) f(1)=1

M) f(1)=2

N) The range is all real numbers less than and equal to 4

Answer 1

Based on the graph of the relation shown above, all of the true statements include;

F) f(-1) = 0.

H) This is a function.

M) f(1) = 2

In Mathematics and Euclidean Geometry, a piecewise-defined function is a type of function that is defined by two or more mathematical expressions over a specific domain.

Note: The inequality symbol < or > represents a hollow dot (circle).

The inequality symbol ≤ or ≥ represents a solid dot (circle).

Generally speaking, the domain of any piecewise-defined function is the union of all of its sub-domains. By critically observing the given piecewise-defined function, we have the following domains;

Domain = x > 1, for f(x) = 4.

Domain = x ≤ 1, for f(x) = x + 1.

Based on the domain, the correct output values for this function include the following;

f(-1) = -1 + 1

f(-1) = 0.

f(1) = 1 + 1

f(1) = 2.

The range of this function is given by;

Range = (-∞, 2] ∪ (4)