Writing Functions from Graphs & Function Operations Warmup

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What does it mean to write a function in standard form?

Back

A function is in standard form when it is expressed as an equation, typically in the form of y = mx + b for linear functions, where m is the slope and b is the y-intercept.

Front

How do you find the sum of two functions, f(x) and g(x)?

Back

To find the sum, you add the outputs of the functions: (f + g)(x) = f(x) + g(x).

Front

What is the difference between f(x) and g(x)?

Back

The difference is found by subtracting the outputs: (f - g)(x) = f(x) - g(x).

Front

How do you multiply two functions, f(x) and g(x)?

Back

To multiply, you multiply the outputs: (f * g)(x) = f(x) * g(x).

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a(b^x), where a is a constant, b is the base, and x is the exponent.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you find the value of a function at a specific point?

Back

To find the value of a function at a specific point, substitute the input value into the function's equation.

Front

What is the significance of the y-intercept in a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, indicating the output value when the input is zero.

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing if its output values rise as the input values increase, and decreasing if its output values fall as the input values increase.