2024 Fall Final Exam Review III.

Front

What is the transformation of the function g(x) = 1/4 f(x) compared to f(x)?

Back

g(x) = 1/4 f(x) represents a vertical compression of the function f(x) by a factor of 1/4.

Front

How do you convert a linear equation from slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to isolate the variables on one side.

Front

What does the slope of a line represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers and A should be non-negative.

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, and x is the exponent.

Front

How do you identify exponential growth from a table of values?

Back

Exponential growth can be identified if the ratio of consecutive y-values is constant as x increases.

Front

What is the effect of shifting a graph vertically?

Back

Shifting a graph vertically changes the y-values of the function without affecting the x-values.

Front

What does it mean for a function to be 'twice as steep'?

Back

A function is 'twice as steep' if its slope is multiplied by 2.

Front

How do you determine the equation of a line given a point and a slope?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay; if the base is greater than 1, the function represents growth; if between 0 and 1, it represents decay.