Evaluate The Given Function: T ( T ) = 7 T + 2 T(t) = 7t + 2 T ( T ) = 7 T + 2 .Find T ( − 4 T T(-4t T ( − 4 T ] And T ( T + 2 T(t+2 T ( T + 2 ].1. T ( − 4 T ) = □ T(-4t) = \square T ( − 4 T ) = □ (Simplify Your Answer. Do Not Factor.)2. T ( T + 2 ) = □ T(t+2) = \square T ( T + 2 ) = □ (Simplify Your Answer. Do Not Factor.)

Mar 12, 2025 by ADMIN 326 views

Evaluating the Function T(t) = 7t + 2

In this article, we will evaluate the given function $T(t) = 7t + 2$ and find the values of $T(-4t)$ and $T(t+2)$ . The function $T(t)$ is a linear function, which means it can be represented in the form $T(t) = mt + b$ , where $m$ is the slope and $b$ is the y-intercept.

To evaluate $T(-4t)$ , we need to substitute $-4t$ into the function $T(t) = 7t + 2$ . This means we will replace every instance of $t$ with $-4t$ .

$T(-4t) = 7(-4t) + 2$

Using the distributive property, we can simplify the expression:

$T(-4t) = -28t + 2$

Therefore, the value of $T(-4t)$ is $-28t + 2$ .

To evaluate $T(t+2)$ , we need to substitute $t+2$ into the function $T(t) = 7t + 2$ . This means we will replace every instance of $t$ with $t+2$ .

$T(t+2) = 7(t+2) + 2$

Using the distributive property, we can simplify the expression:

$T(t+2) = 7t + 14 + 2$

Combining like terms, we get:

$T(t+2) = 7t + 16$

Therefore, the value of $T(t+2)$ is $7t + 16$ .

In this article, we evaluated the given function $T(t) = 7t + 2$ and found the values of $T(-4t)$ and $T(t+2)$ . We used the distributive property to simplify the expressions and found that $T(-4t) = -28t + 2$ and $T(t+2) = 7t + 16$ . These results demonstrate the importance of understanding function notation and how to evaluate expressions with variables.

The function $T(t) = 7t + 2$ is a linear function.
To evaluate $T(-4t)$ , we substitute $-4t$ into the function and simplify the expression.
To evaluate $T(t+2)$ , we substitute $t+2$ into the function and simplify the expression.
The value of $T(-4t)$ is $-28t + 2$ .
The value of $T(t+2)$ is $7t + 16$ .

Evaluating functions is an essential skill in mathematics, and it requires a deep understanding of function notation and algebraic manipulation. By following the steps outlined in this article, you can evaluate functions with variables and simplify expressions to find the desired values.
Evaluating the Function T(t) = 7t + 2: Q&A

In our previous article, we evaluated the given function $T(t) = 7t + 2$ and found the values of $T(-4t)$ and $T(t+2)$ . In this article, we will answer some frequently asked questions (FAQs) related to evaluating functions and provide additional examples to help you understand the concepts better.

A: A linear function is a function that can be represented in the form $f(x) = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. A non-linear function, on the other hand, is a function that cannot be represented in this form. Examples of non-linear functions include quadratic functions, polynomial functions, and exponential functions.

A: To evaluate a function with a variable in the exponent, you need to use the properties of exponents. For example, if you have a function like $f(x) = 2^x$ , you can evaluate it by substituting the value of $x$ into the exponent. For example, if $x = 3$ , then $f(3) = 2^3 = 8$ .

A: Yes, you can use the distributive property to evaluate a function with multiple variables. For example, if you have a function like $f(x, y) = 2x + 3y$ , you can evaluate it by distributing the coefficients to each variable. For example, if $x = 2$ and $y = 3$ , then $f(2, 3) = 2(2) + 3(3) = 4 + 9 = 13$ .

A: To evaluate a function with a negative coefficient, you need to follow the same steps as evaluating a function with a positive coefficient. For example, if you have a function like $f(x) = -2x + 3$ , you can evaluate it by substituting the value of $x$ into the function. For example, if $x = 2$ , then $f(2) = -2(2) + 3 = -4 + 3 = -1$ .

A: Yes, you can use the order of operations to evaluate a function with multiple operations. For example, if you have a function like $f(x) = 2x + 3 - 4$ , you can evaluate it by following the order of operations: parentheses, exponents, multiplication and division, and addition and subtraction. For example, if $x = 2$ , then $f(2) = 2(2) + 3 - 4 = 4 + 3 - 4 = 3$ .

A: To evaluate a function with a variable in the denominator, you need to follow the same steps as evaluating a function with a variable in the numerator. For example, if you have a function like $f(x) = 2/x$ , you can evaluate it by substituting the value of $x$ into the function. For example, if $x = 2$ , then $f(2) = 2/2 = 1$ .

In this article, we answered some frequently asked questions related to evaluating functions and provided additional examples to help you understand the concepts better. We hope that this article has been helpful in clarifying any doubts you may have had about evaluating functions. If you have any further questions or need additional help, please don't hesitate to ask.

A linear function is a function that can be represented in the form $f(x) = mx + b$ .
To evaluate a function with a variable in the exponent, you need to use the properties of exponents.
You can use the distributive property to evaluate a function with multiple variables.
To evaluate a function with a negative coefficient, you need to follow the same steps as evaluating a function with a positive coefficient.
You can use the order of operations to evaluate a function with multiple operations.
To evaluate a function with a variable in the denominator, you need to follow the same steps as evaluating a function with a variable in the numerator.