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Ontario Tech acknowledges the lands and people of the Mississaugas of Scugog Island First Nation.

We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

Learn more about Indigenous Education and Cultural Services

Domain and Range of Exponential and Logarithmic Functions

The domain of a function is the specific set of values that the independent variable in a function can take on. The range is the resulting values that the dependant variable can have as x varies throughout the domain.

Finding the domain/range

When determining domain it is more convenient to determine where the function would not exist. For example, we can only take the logarithm of values greater than 0. However, its range is such that y ∈ R. Remember that logarithmic functions and exponential functions are inverse functions, so as expected, the domain of an exponential is such that x ∈ R, but the range will be greater than 0.

Domain and Range graphs

Example: Find the domain and range for f(x) = In(x + 5)

Solution:

Domain                                   Range

x + 5 > 0                                  y ∈ R

      x > -5

Example: Find the domain and range for f(x) = 1/ (e- 1)

Solution:

Domain                                   Range

ex – 1 ≠ 0                                 y ≠ 0

       ex ≠ 1

 ln(ex) ≠ ln(1)

        x ≠ 0

Example 1:

Example 2: