Writing Exponential Equations Practice

Writing Exponential Functions

1) Find the starting value, where x = 0

2) Divide y₂/y₁ to find the growth or decay factor

3) Write as y = ab^x

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From a Table

Math Response

Write the equation of the table given in the form

y= ab^x

Type answer here

Correct Answer: y=2\left(3\right)^x

Deg^°

Rad

Math Response

Write the equation of the table given in the form

y= ab^x

Type answer here

Correct Answer: y=4\left(\frac{1}{2}\right)^x

Deg^°

Rad

Math Response

Write the equation of the table given in the form

y= ab^x

Type answer here

Correct Answer: y=-2\left(\frac{4}{3}\right)^x

Deg^°

Rad

Math Response

Write the equation of the table given in the form

y= ab^x

Type answer here

Correct Answer: y=-4\left(3\right)^x

Deg^°

Rad

• Going up is a + direction so k is positive when we go up

• Going down is a - direction so k is negative when we go down

​Vertical

• When we go left - (-#) becomes positive, so it looks like x + h

• When we go right - (#) so it looks like x - h

Horizontal

Translations using
y= a⋅b ^x-h + k

Multiple Choice

If we know $$f\left(x\right)=2^x$$ , what is the equation when we have a translation 3 units down?

• $$y=2^{\left(x-3\right)}$$

• $$y=2^{\left(x+3\right)}$$

• $$y=2^x-3$$

• $$y=2^x+3$$

Multiple Choice

If we know $$f\left(x\right)=2^x$$ , what is the equation when we have a translation 3 units right?

• $$y=2^{\left(x-3\right)}$$

• $$y=2^{\left(x+3\right)}$$

• $$y=2^x-3$$

• $$y=2^x+3$$

Math Response

What would be the equation of a function that is shifted left 14 units and up 32 units from f(x) = 4^x?

Type answer here

Correct Answer: y=4^{\left(x+14\right)}+32

Deg^°

Rad

• New function will have a negative in front of the x inside parenthesis

• f(-x)

Across the y-axis

• New function will start with a negative out front.

• -f(x)

Across the x-axis

Reflections

Dropdown

For the graph below a reflection occurred over the ​

Select answer

Dropdown

For the graph below a reflection occurred over the ​

Select answer

Multiple Choice

Which is the equation that represents the transform graphed from the solid black function to match the dotted function?

• -f(x-4)+3

• -f(x+4)+3

• f(-x+4)+3

• f(-x-4)+3

Multiple Choice

Which is the equation that represents the transform graphed from the solid black function to match the dotted function?

• -f(x)-2

• -f(x) +2

• f(-x) - 2

• f(-x) + 2

Multiple Choice

The graph of y = f(x) is the solid black graph given. Write a function that represents the orange dotted graph.

• $$f\left(x+4\right)+1$$

• $$f\left(x-4\right)+1$$

• $$f\left(x+1\right)+4$$

• $$f\left(x-4\right)+1$$