Algebra 1A - FINAL REVIEW

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How do you write a linear function for a fixed charge plus additional charges?

Back

The function can be written as f(x) = mx + b, where m is the cost per additional item (charm) and b is the fixed charge.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Front

How do you calculate the population after a certain number of years with exponential growth?

Back

Use the formula y = a(1 + r)^t, substituting a for the initial population, r for the growth rate, and t for the number of years.

Front

What is the difference between a linear function and an exponential function?

Back

A linear function increases by a constant amount, while an exponential function increases by a constant percentage.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function; it indicates how much the output (y) changes for a unit change in the input (x).

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the value of the function when x = 0; it represents the starting point of the function on the y-axis.

Front

How do you determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the significance of the fixed charge in a pricing model?

Back

The fixed charge is the base cost that must be paid regardless of the number of additional items or services.

Front

How do you write a linear equation for hourly wages plus tips?

Back

The equation can be written as f(h) = wh + t, where w is the hourly wage, h is the number of hours worked, and t is the total tips.