Understanding Functions Quiz

Which of the following best defines a function?

• A relationship where each input has multiple possible outputs

• A relationship where each input corresponds to exactly one output

• A mathematical set with no specific mapping rules

• A graph that is always a straight line

If a vertical line intersects a graph at more than one point, what does this indicate about the graph?

• The graph represents a function

• The graph fails the vertical line test

• The graph has a linear relationship

• The graph has a constant slope

Which of the following is an example of a one-to-one function?

• f(x) = x²

• f(x) = |x|

• f(x) = x³

• f(x) = x + 5

For the function f(x) = 2x + 3, what is the domain if the range is restricted to real numbers between 0 and 10?

• {x | -1.5 ≤ x ≤ 3.5}

• {x | 0 ≤ x ≤ 5}

• {x | -3.5 ≤ x ≤ 1.5}

• {x | -5 ≤ x ≤ 5}

Which type of function always passes through the origin (0,0)?

• Quadratic function

• Exponential function

• Direct variation function

• Logarithmic function

What characteristic distinguishes a bijective function?

• It is both injective and surjective

• It has a constant rate of change

• It is always increasing

• It passes through the origin

For the function f(x) = √(x - 2), what is the domain?

• All real numbers

• {x | x ≥ 2}

• {x | x > 2}

• {x | x ≤ 2}

Which transformation would NOT change a function's fundamental characteristics?

• Horizontal translation

• Vertical stretch

• Horizontal reflection

• Vertical translation

In the relation {(1,2), (3,4), (5,6), (1,7)}, is this a function?

• Yes, because it has unique x-coordinates

• No, because 1 maps to two different y-values

• Yes, because all coordinates are positive

• No, because the pairs are not ordered

What does the range represent in a function?

• All possible input values

• All possible output values

• The midpoint of the function

• The maximum value of the function