Create Functions from Tables & Graphs

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as an equation, a table, or a graph.

Tags

CCSS.8.F.A.1

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a(b)^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent.

Front

How do you determine the equation of a line from a graph?

Back

To determine the equation of a line from a graph, identify the slope (rise over run) and the y-intercept (where the line crosses the y-axis). Use the slope-intercept form: y = mx + b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Tags

CCSS.8.EE.B.5

Front

What is a y-intercept?

Back

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

Front

How can you write a function from a table of values?

Back

To write a function from a table, look for patterns in the x and y values. Determine if the relationship is linear, quadratic, or exponential, and then derive the function.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change and are represented by straight lines, while exponential functions have a variable rate of change and are represented by curves.

Front

What is the equation of a line with a slope of -3 and a y-intercept of -3?

Back

The equation of the line is y = -3x - 3.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How do you find the slope from two points?

Back

The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Tags

CCSS.8.EE.B.5

Front

What is the equation of a line with a slope of (3/5) and a y-intercept of 1?

Back

The equation of the line is y = (3/5)x + 1.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3