Review of Graphing Exponentials

Review of Graphing Exponentials

Solidify our understanding of the properties of an exponential function. Preparing for logarithms as inverses of exponentials.

Multiple Select

A parent function is a function in its simpliest form. For example, y = x is the parent function of a line. y = 2x changes the slant of the line and y = x - 2 shifts the line down 2 units. y = b^x is the parent function for an exponential. Given y = 3^x ; which of the following is true?

• The y - intercept is (0, 3).

• The decay rate is 1/3.

• The growth rate is 3.

• All of the above are true.

Multiple Select

A parent function is a function in its simpliest form. For example, y = x is the parent function of a line. y = 2x changes the slant of the line and y = x - 2 shifts the line down 2 units. y = b^x is the parent function for an exponential. Given y = 5*3^x ; which of the following is true? Select all that apply.

• The y - intercept is (0, 5).

• The decay rate is 1/3.

• The growth rate is 3.

• The point (1, 15) lies on the function.

Order of operations tells us that we need to simplify a power first. If there is a value in the "h" position that is our first movement to out key points.

**Remember - ask yourself the question what value of x makes x - h equal to zero?

Fill in the Blank

Given y = 2*4^{x + 2}; what is the horizontal shift? The shift is 2 units to the ______.

Fill in the Blank

Given y = 2*4^{x + 2}; what is the horizontal shift? The y - intercept is (0,2) - the (0,a) point. What is the coordinate point when the horizontal shift is applied?

Multiple Choice

Given y = (1/4)*8^x-3 ; which points represent the correct movement from parent function to point on function after the transformation.

• (1, 2) moves to (1, 5)

• (1, 2) moves to (4, 2)

• (1, 8) moves to (4, 8)

• None of these are correct

The "k" value is the LAST step we would take in simplifiying. You plug in x to find y; multiplication first then addition (or subtraction)

**Remember - the "k" is your new range and asymptote.

Fill in the Blank

Given y=2*(1/8)^x + 4; the range of the function would be y > ___.

Fill in the Blank

Given y=2*(1/8)^x + 4; the y - intercept of the parent function (y=2*(1/8)^x) would be (0, 2). What is the new coordinate for the y - intercept after the vertical shift is applied?

Multiple Choice

Given y = 3*5^x - 6; which of the following is the correct movement from the parent function to the graph?

• (1, 15) to (1, 21)

• (1, 8) to (1, 2)

• (1, 15) to (1, 9)

• (1, 8) to (1, 14)

A negative "a" is a reflection over the x - axis while a negative "x" is a reflection over the y - axis.

Fill in the Blank

If the point (0, 2) lies on the function y = 2*3^x then the point ___ lies on y = -2*3^x .

Fill in the Blank

If the point (1, 14) lies on the graph of y = 2*7^x ; then the point ___ lies on the graph of y = 2*7^-x .

Multiple Select

Which of the following is true about the graph of y = 3*9^x+1 - 4? Select all that apply.

• The shift of the parent function is 1 unit right.

• The shift of the parent function is 4 units down

• The point (0,23) is a point on the function.

• The range of the function is y > -4.

Multiple Choice

Which of the following is the equation of the graph at left?

• y = 3*(1/3)^x-1 - 2

• y = 3*(1/3)^x+1 + 2

• y = 3*(1/3)^x-1 + 2

• None of these work