Comparing Functions TEST

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time. It can be represented by the function f(x) = a(1 + r)^x.

Front

How do you determine if a function is linear, exponential, or quadratic?

Back

You can determine the type of function by analyzing its rate of change: linear functions have a constant rate of change, exponential functions have a variable rate of change that increases, and quadratic functions have a rate of change that itself changes.

Front

What is the difference between linear growth and exponential growth?

Back

Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a percentage of the current value, leading to faster growth over time.

Front

If Jeremy chooses Plan 1, how much will he earn after 12 days?

Back

Plan 1: $6.00 + ($0.50 * 11) = $6.00 + $5.50 = $11.50.

Front

If Jeremy chooses Plan 2, how much will he earn after 12 days?

Back

Plan 2: $0.01 doubled for 12 days = $0.01 * 2^11 = $0.01 * 2048 = $20.48.

Front

What does a scatter plot showing linear growth look like?

Back

A scatter plot showing linear growth will have points that form a straight line or close to a straight line, indicating a constant rate of change.

Front

What is a constant rate of change?

Back

A constant rate of change means that for every unit increase in x, the value of y increases by a fixed amount.

Front

What is the formula for calculating the slope of a linear function?

Back

The slope (m) of a linear function can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, which graphs as a parabola.