Select the correct answer.
Find the value of [tex]f(-3)[/tex] for the function below.
[tex]f(x)=2 x+10[/tex]
A. -4
B. -6.5
C. 4
D. 16
Answer (2)
Substitute x = − 3 into the function f ( x ) = 2 x + 10 .
Calculate 2 × ( − 3 ) = − 6 .
Add − 6 and 10 to get 4 .
The value of f ( − 3 ) is 4 .
Explanation
Understanding the problem We are given the function f ( x ) = 2 x + 10 and asked to find the value of f ( − 3 ) . This means we need to substitute − 3 for x in the expression 2 x + 10 .
Substituting x = -3 Now, let's substitute x = − 3 into the function: f ( − 3 ) = 2 ( − 3 ) + 10
Performing the multiplication Next, we perform the multiplication: f ( − 3 ) = − 6 + 10
Adding the numbers Finally, we add the numbers: f ( − 3 ) = 4
Final Answer Therefore, the value of f ( − 3 ) is 4.
Examples
Imagine you are tracking the temperature change throughout the day. If the temperature at a certain time is given by the function f ( x ) = 2 x + 10 , where x is the number of hours since midnight, then finding f ( − 3 ) would represent the temperature 3 hours before midnight. This kind of calculation is useful in many real-world scenarios, such as predicting weather patterns, calculating financial growth, or determining the trajectory of a moving object. Understanding how to evaluate functions for specific inputs allows us to make predictions and informed decisions based on mathematical models.
To find f ( − 3 ) for the function f ( x ) = 2 x + 10 , we substitute − 3 into the function, leading to f ( − 3 ) = 4 . Therefore, the correct answer is option C: 4.
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