Answer:
Function notation is a way to represent a function using symbols. It is often used to evaluate a function at a specific value, and to write and interpret expressions that involve functions.
To write a function using function notation, we typically use the following format:
f(x) = y
Here, f is the name of the function, x is the input, and y is the output. For example, we could define a function f(x) = 2x + 1, which takes an input value x, multiplies it by 2, and adds 1 to get the output value y.
To evaluate a function using function notation, we simply plug in the input value into the function and simplify. For example, if we want to find f(3) for the function f(x) = 2x + 1, we plug in x = 3 and get:
f(3) = 2(3) + 1
f(3) = 7
So the output value when the input is 3 is 7.
We can also use function notation to write expressions that involve functions. For example, we could write an expression g(x) = f(x) + 3, which adds 3 to the output value of the function f for any input value x. We could also interpret an expression such as f(5) + f(7) as the sum of the output values of the function f when the input is 5 and when the input is 7.
Interpreting expressions with function notation involves understanding what the expression represents in terms of the function and its input/output values. Writing expressions with function notation involves using the function notation to represent relationships between functions and their input/output values.
For example, suppose we have a function f(x) = x^2 + 3x - 2. We could interpret the expression f(4) as the output value of the function f when the input value is 4. Plugging in x = 4 into the function, we get:
f(4) = (4)^2 + 3(4) - 2
f(4) = 16 + 12 - 2
f(4) = 26
So f(4) = 26, which is the output value of the function when the input value is 4.
We can also write expressions with function notation to represent relationships between functions and their input/output values. For example, suppose we want to define a new function g(x) that is equal to twice the value of f(x) minus 5. We could write this using function notation as:
g(x) = 2f(x) - 5
Here, we are using the function notation to represent the relationship between the function g and the function f, where g is defined in terms of f. To evaluate g(2) using this expression, we first need to find the value of f(2):
f(2) = (2)^2 + 3(2) - 2
f(2) = 6
Then, we can plug this value into the expression for g(x):
g(2) = 2f(2) - 5
g(2) = 2(6) - 5
g(2) = 7
So g(2) = 7, which is the output value of the function g when the input value is 2.