Evaluate Each Function.1) K ( A ) = A 2 + 2 A K(a) = A^2 + 2a K ( A ) = A 2 + 2 A ; Find K ( − 9 K(-9 K ( − 9 ]2) G ( A ) = 3 A + 3 G(a) = 3a + 3 G ( A ) = 3 A + 3 ; Find G ( − 6 G(-6 G ( − 6 ]3) K ( X ) = − 2 X 2 + 5 X K(x) = -2x^2 + 5x K ( X ) = − 2 X 2 + 5 X ; Find K ( 10 K(10 K ( 10 ]4) H ( X ) = X + 2 H(x) = X + 2 H ( X ) = X + 2 ; Find H ( − 9 H(-9 H ( − 9 ]

Introduction

Functions are a fundamental concept in mathematics, and evaluating them is a crucial skill to master. In this article, we will explore the process of evaluating functions, and we will apply this knowledge to four different functions. We will learn how to substitute values into functions, simplify expressions, and find the output values.

What is a Function?

A function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. It is a rule that assigns to each input exactly one output. In other words, for every input, there is only one output. Functions can be represented graphically, algebraically, or verbally.

Evaluating Functions

To evaluate a function, we need to substitute a value into the function and simplify the expression. The value we substitute is called the input or the argument, and the output is called the value of the function.

Example 1: Evaluating $k(a) = a^2 + 2a$

Let's evaluate the function $k(a) = a^2 + 2a$ at $a = -9$.

Step 1: Substitute the value of $a$ into the function

$k(-9) = (-9)^2 + 2(-9)$

Step 2: Simplify the expression

$k(-9) = 81 - 18$

Step 3: Evaluate the expression

$k(-9) = 63$

Therefore, $k(-9) = 63$.

Example 2: Evaluating $g(a) = 3a + 3$

Let's evaluate the function $g(a) = 3a + 3$ at $a = -6$.

Step 1: Substitute the value of $a$ into the function

$g(-6) = 3(-6) + 3$

Step 2: Simplify the expression

$g(-6) = -18 + 3$

Step 3: Evaluate the expression

$g(-6) = -15$

Therefore, $g(-6) = -15$.

Example 3: Evaluating $k(x) = -2x^2 + 5x$

Let's evaluate the function $k(x) = -2x^2 + 5x$ at $x = 10$.

Step 1: Substitute the value of $x$ into the function

$k(10) = -2(10)^2 + 5(10)$

Step 2: Simplify the expression

$k(10) = -200 + 50$

Step 3: Evaluate the expression

$k(10) = -150$

Therefore, $k(10) = -150$.

Example 4: Evaluating $h(x) = x + 2$

Let's evaluate the function $h(x) = x + 2$ at $x = -9$.

Step 1: Substitute the value of $x$ into the function

$h(-9) = -9 + 2$

Step 2: Simplify the expression

$h(-9) = -7$

Step 3: Evaluate the expression

$h(-9) = -7$

Therefore, $h(-9) = -7$.

Conclusion

Evaluating functions is a crucial skill in mathematics, and it requires attention to detail and a clear understanding of the function's definition. By following the steps outlined in this article, you can evaluate functions with confidence. Remember to substitute values into the function, simplify expressions, and find the output values. With practice, you will become proficient in evaluating functions and solving problems involving functions.

Key Takeaways

• A function is a relation between a set of inputs and a set of possible outputs.
• To evaluate a function, substitute a value into the function and simplify the expression.
• The value we substitute is called the input or the argument, and the output is called the value of the function.
• Functions can be represented graphically, algebraically, or verbally.

Practice Problems

1. Evaluate the function $f(x) = 2x^2 - 3x$ at $x = 4$.
2. Evaluate the function $g(x) = x^2 + 2x$ at $x = -3$.
3. Evaluate the function $h(x) = -x^2 + 5x$ at $x = 2$.
4. Evaluate the function $k(x) = x + 1$ at $x = -2$.

Answer Key

1. $f(4) = 2(4)^2 - 3(4) = 32 - 12 = 20$
2. $g(-3) = (-3)^2 + 2(-3) = 9 - 6 = 3$
3. $h(2) = -(2)^2 + 5(2) = -4 + 10 = 6$
4. $k(-2) = -2 + 1 = -1$
   Evaluating Functions: A Q&A Guide =====================================

Introduction

Evaluating functions is a crucial skill in mathematics, and it requires attention to detail and a clear understanding of the function's definition. In this article, we will answer some frequently asked questions about evaluating functions, and provide examples to help you understand the concepts.

Q: What is a function?

A: A function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. It is a rule that assigns to each input exactly one output.

Q: How do I evaluate a function?

A: To evaluate a function, you need to substitute a value into the function and simplify the expression. The value you substitute is called the input or the argument, and the output is called the value of the function.

Q: What is the difference between the input and the output?

A: The input is the value you substitute into the function, and the output is the value of the function after simplification.

Q: Can I evaluate a function with a variable?

A: Yes, you can evaluate a function with a variable. For example, if you have the function $f(x) = 2x^2 - 3x$ and you want to evaluate it at $x = 4$, you would substitute $x = 4$ into the function and simplify the expression.

Q: How do I handle negative numbers when evaluating a function?

A: When evaluating a function with a negative number, you need to follow the order of operations (PEMDAS) and simplify the expression. For example, if you have the function $f(x) = 2x^2 - 3x$ and you want to evaluate it at $x = -4$, you would substitute $x = -4$ into the function and simplify the expression.

Q: Can I evaluate a function with a fraction?

A: Yes, you can evaluate a function with a fraction. For example, if you have the function $f(x) = 2x^2 - 3x$ and you want to evaluate it at $x = \frac{1}{2}$, you would substitute $x = \frac{1}{2}$ into the function and simplify the expression.

Q: How do I handle exponents when evaluating a function?

A: When evaluating a function with exponents, you need to follow the order of operations (PEMDAS) and simplify the expression. For example, if you have the function $f(x) = 2x^2 - 3x$ and you want to evaluate it at $x = 2^3$, you would substitute $x = 2^3$ into the function and simplify the expression.

Q: Can I evaluate a function with a trigonometric function?

A: Yes, you can evaluate a function with a trigonometric function. For example, if you have the function $f(x) = 2\sin(x) - 3\cos(x)$ and you want to evaluate it at $x = \frac{\pi}{4}$, you would substitute $x = \frac{\pi}{4}$ into the function and simplify the expression.

Q: How do I handle absolute value when evaluating a function?

A: When evaluating a function with absolute value, you need to follow the definition of absolute value and simplify the expression. For example, if you have the function $f(x) = |x| + 2$ and you want to evaluate it at $x = -3$, you would substitute $x = -3$ into the function and simplify the expression.

Conclusion

Evaluating functions is a crucial skill in mathematics, and it requires attention to detail and a clear understanding of the function's definition. By following the steps outlined in this article, you can evaluate functions with confidence. Remember to substitute values into the function, simplify expressions, and find the output values. With practice, you will become proficient in evaluating functions and solving problems involving functions.

Key Takeaways

• A function is a relation between a set of inputs and a set of possible outputs.
• To evaluate a function, substitute a value into the function and simplify the expression.
• The value you substitute is called the input or the argument, and the output is called the value of the function.
• Functions can be represented graphically, algebraically, or verbally.

Practice Problems

1. Evaluate the function $f(x) = 2x^2 - 3x$ at $x = 4$.
2. Evaluate the function $g(x) = x^2 + 2x$ at $x = -3$.
3. Evaluate the function $h(x) = -x^2 + 5x$ at $x = 2$.
4. Evaluate the function $k(x) = x + 1$ at $x = -2$.

Answer Key

1. $f(4) = 2(4)^2 - 3(4) = 32 - 12 = 20$
2. $g(-3) = (-3)^2 + 2(-3) = 9 - 6 = 3$
3. $h(2) = -(2)^2 + 5(2) = -4 + 10 = 6$
4. $k(-2) = -2 + 1 = -1$