Given the function $$f(x) = 3x - 12$$ , what is $$f(2)$$ ?

$$f(2) = 3(2) - 12 = 6 - 12 = -6$$ .

If $$f(x) = -\frac{3}{2}x + 5$$ , what is $$f(2)$$ ?

$$f(2) = -\frac{3}{2}(2) + 5 = -3 + 5 = 2$$ .

Given $$h(x) = 3x^2 - 2x + 8$$ , what is $$h(2)$$ ?

$$h(2) = 3(2^2) - 2(2) + 8 = 3(4) - 4 + 8 = 12 - 4 + 8 = 16$$ .

What is a quadratic function?

A quadratic function is a function that can be expressed in the form $$f(x) = ax^2 + bx + c$$ , where $$a$$ , $$b$$ , and $$c$$ are constants and @@a eq 0@@.

Is the relation defined by pairs (1,2), (1,3), (2,4) a function? Why?

No, because the x-value 1 has two different y-values (2 and 3) associated with it.

What is the y-intercept of the function $$f(x) = 3x - 12$$ ?

The y-intercept is -12, which is the value of $$f(0)$$ .

What is the domain of the function $$f(x) = \frac{1}{x}$$ ?

The domain is all real numbers except for x = 0, since division by zero is undefined.

What is the range of the function $$f(x) = x^2$$ ?

The range is all real numbers greater than or equal to 0, since a square of a real number cannot be negative.

Given $$f(x) = 2x + 3$$ , what is the value of $$x$$ when $$f(x) = 7$$ ?

Set $$2x + 3 = 7$$ . Solving gives $$2x = 4$$ , so $$x = 2$$ .

What is the difference between a function and a relation?

A relation is any set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

2.

FLASHCARD QUESTION

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a graph of a function. If any vertical line intersects the curve more than once, then the curve is not a function.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value).

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the definition of a linear function?

Back

7.

FLASHCARD QUESTION

Front

Back

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