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Common Core: High School - Functions : Function Notation: CCSS.Math.Content.HSF-IF.A.2

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Example Question #21 : Interpreting Functions

For the function , calculate the function value at negative five.

$f(x)=5x-\frac{100-x}{5}$

Possible Answers:

f(5)=9

f(-5)=45

f(-5)=-46

f(5)=7

f(-5)=10

Correct answer:

f(-5)=-46

Explanation:

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form f(x) and the question asks to calculate f(-5) we know that the input value is negative five.

$f(-5)\rightarrow x=-5$

Step 2: Given the function, input the desired value.

In step one the input value of negative five was found. Now substitute -5 in for every in the function.

$f(x)=5x-\frac{100-x}{5}$

$f(-5)=5(-5)-\frac{100--5}{5}$

$f(-5)=-25-\frac{105}{5}$

$f(-5)=-25-\frac{21\cdot 5}{5}$

f(-5)=-25-21

f(-5)=-46

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Example Question #12 : Function Notation: Ccss.Math.Content.Hsf If.A.2

Given the following function , calculate f(3) .

$f(x)=\frac{1}{x}+\sqrt{3x-5}$

Assume is always positive.

Possible Answers:

$f(3)=\frac{4}{3}$

f(3)=2

$f(3)=\frac{9}{3}$

$f(3)=\frac{7}{3}$

$f(3)=\frac{5}{3}$

Correct answer:

$f(3)=\frac{7}{3}$

Explanation:

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.Math.content.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form f(x) and the question asks to calculate f(3) we know that the input value is three.

$f(3)\rightarrow x=3$

Step 2: Given the function, input the desired value.

In step one the input value of three was found. Now substitute 3 in for every in the function.

$\\f(x)=\frac{1}{x}+\sqrt{3x-5} \\ \\f(3)=\frac{1}{3}+\sqrt{3(3)-5} \\ \\ f(3)=\frac{1}{3}+\sqrt{9-5} \\ \\f(3)=\frac{1}{3}+\sqrt{4} \\ \\f(3)=\frac{1}{3}+ 2 \\ \\f(3)=\frac{7}{3}$

Step 3: Answer the question.

The answer is

$f(3)=\frac{7}{3}$

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Common Core: High School - Functions : Function Notation: CCSS.Math.Content.HSF-IF.A.2

Study concepts, example questions & explanations for Common Core: High School - Functions

All Common Core: High School - Functions Resources

Example Questions

Example Question #21 : Interpreting Functions

Example Question #12 : Function Notation: Ccss.Math.Content.Hsf If.A.2

All Common Core: High School - Functions Resources

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