Topic 5 Grade Improvement

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 y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = ab^x, where a is a constant, b is the base (a positive real number), and x is the exponent. It represents growth or decay.

Front

What does the term 'y-intercept' mean?

Back

The y-intercept is the point where a graph intersects the y-axis. It is the value of y when x = 0.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base of the exponential function is greater than 1 (b > 1), while exponential decay occurs when the base is between 0 and 1 (0 < b < 1).

Tags

CCSS.HSF-IF.C.8B

Front

How do you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are constant, the function is linear.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the transformation 'right 3' mean in a function?

Back

The transformation 'right 3' means that the graph of the function is shifted 3 units to the right on the x-axis. For example, f(x) = 2^(x-3) is shifted right by 3.

Tags

CCSS.HSF.BF.B.3

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Tags

CCSS.8.EE.B.5

Front

How can you determine if a function is exponential from its equation?

Back

If the equation can be expressed in the form y = ab^x, where b is a constant greater than 0, then it is an exponential function.

Front

What does it mean for a function to have a y-intercept of 3?

Back

A function with a y-intercept of 3 means that when x = 0, the value of y is 3. This is the point (0, 3) on the graph.