About Graphs of Functions:
We need to be able to identify the graphs of basic functions. The identity function, y = x, the squaring function, y = x2, the cubing function, y = x3, the square root function, y = sqrt(x), the cube root function, y = cbrt(x), and the reciprocal function, y = 1/x. We also need to be familiar with the domain and range for each function.
Test Objectives
- Demonstrate the ability to sketch the graph of a function
- Demonstrate the ability to find the domain of a function based on its graph
- Demonstrate the ability to find the range of a function based on its graph
#1:
Instructions: graph each, state the domain and range.
$$a)\hspace{.2em}f(x)=x$$
$$b)\hspace{.2em}f(x)=x^2$$
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#2:
Instructions: graph each, state the domain and range.
$$a)\hspace{.2em}f(x)=x^3$$
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#3:
Instructions: graph each, state the domain and range.
$$a)\hspace{.2em}f(x)=\sqrt{x}$$
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#4:
Instructions: graph each, state the domain and range.
$$a)\hspace{.2em}f(x)=\sqrt[3]{x}$$
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#5:
Instructions: graph each, state the domain and range.
$$a)\hspace{.2em}f(x)=\frac{1}{x}$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}$$ $$\text{Domain}: (-\infty, \infty)$$ $$\text{Range}: (-\infty, \infty)$$
$$b)\hspace{.2em}$$ $$\text{Domain}: (-\infty, \infty)$$ $$\text{Range}: [0, \infty)$$
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#2:
Solutions:
$$a)\hspace{.2em}$$ $$\text{Domain}: (-\infty, \infty)$$ $$\text{Range}: (-\infty, \infty)$$
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#3:
Solutions:
$$a)\hspace{.2em}$$ $$\text{Domain}: [0, \infty)$$ $$\text{Range}: [0, \infty)$$
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#4:
Solutions:
$$a)\hspace{.2em}$$ $$\text{Domain}: (-\infty, \infty)$$ $$\text{Range}: (-\infty, \infty)$$
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#5:
Solutions:
$$a)\hspace{.2em}$$ $$\text{Domain}: (-\infty, 0) ∪ (0, \infty)$$ $$\text{Range}: (-\infty, 0) ∪ (0, \infty)$$
