Exponential and Log Functions

Characteristics

100

Determine the end behaviour of the following: 

y = -3 log x 

QI-QIV

200

Determine the y-intercept of

y = 3^x

1

300

State the domain of the following: 

y= 7 log x 

{x|x>0,XER} 

400

State the range of:

y = 3 (0.5)^x

{y|y>0,YER} 

500

Determine the y intercept of the following: 

x   1    2    3      4       5 

y   2    8   32   128    512

1/2

Miscellaneous

100

Write 7^-4 with a positive exponent. 

1/7⁴

200

The type of function that always has QII-QI end behaviour? 

Exponential

300

The value of a house grows by 5% per year. The house was purchased for $253,000. What is the equation that represents this function? 

y = 253,000 (1.05)^x

400

Which of the following is/are exponential functions? 

a) y=5^x   b) y=x^0.5    c) y=x³   d) y=3(1/3)^x

a, d 

500

Determine the following for y = -3log x 

End behaviour

#x-intercepts 

y-intercept 

Domain

Range 

QI-QIV

1

N/A

{x|x>0,XER}

{y|yER} 

Exponential

100

Increasing or decreasing: 

y = 5 (0.75)^x

Decreasing 

200

Determine the value of y = 4 (5)^x​

when x=3

​​​

500

300

What's the missing value? 

x  1   2  3    4     5        6       7

y  2  6  18  54    __     486   1458

162

400

Determine the exponential Equation of the following 

x    1     2     3    4     5  

y  324  108  36  12    4 

y = 972 (1/3)^x

500

A car depreciates at 7% per year. If you bought the car for $37,500, what is the value of the car after 9 years? To the nearest dollar. 

$19,515

Logarithmic

100

Evaluate log₃ 81

4

200

State the end behaviour of the following: 

y = 0.5 log x

QIV-QI

300

Determine the y-intercept of the following: 

y = 6 log x

No y-intercept. 

400

End behaviour of: 

positive log: 

negative log: 

positive: QIV-QI 

negative: QI-QIV

500

Evaluate: 

log₃ 387,420,489

18