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Question 1 of 10

1. Question

State whether $y=1$ is a function or not.

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Hint

The relation is a function if each vertical line cuts the graph no more than once.

Question 2 of 10

2. Question

Given \(f\left( x \right) = ax + b\), \(f\left( 0 \right) = 1\) \(f\left( 1 \right) = -1\) and \(f\left( 2 \right) = -1\), find \(a \) and \(b\).

\(a = \) \(b = \) \(c = \)

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Question 3 of 10

3. Question

Find the vertical asymptote(s) of \(f\left( x \right) = \dfrac{1}{{{x^2} – 1}}\).

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Question 4 of 10

4. Question

Given \(f\left( x \right) = 2x – 1\), \(g\left( x \right) = x + 1\), \(\left( {f \circ f} \right)\left( 2 \right) = a\), \(\left( {g \circ f} \right)\left( 1 \right) = b\), \(\left( {f \circ g} \right)\left( c \right) = 3\) and \(\left( {g \circ g} \right)\left( d \right) = 1\) find the domain and range of \(a + b + c + d\).

\(a + b + c + d = \)

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Hint

\(\left( {f \circ g} \right)\left( x \right) = f\left( {g\left( x \right)} \right)\)

Question 5 of 10

5. Question

Find the proper expression of the graph.

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Question 6 of 10

6. Question

If \(f\left( x \right) = 3{x^2} + 2\), find \(2f\left( {x + 2} \right) – 1\) in simplest form.

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Question 7 of 10

7. Question

Choose vector quantities.

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Question 8 of 10

8. Question

Find the vector equation of the following diagram.

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Question 9 of 10

9. Question

Given \(\vec a = \left( {\begin{array}{*{20}{c}} 4\\ 5 \end{array}} \right)\) and \(\vec b = \left( {\begin{array}{*{20}{c}} { – 2}\\ 3 \end{array}} \right)\), find \(\left| {\vec a – \vec b} \right|\), correcting to two significant figures.

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Question 10 of 10

10. Question

Find the coordinates \(\left( {a,b,c} \right)\) of the point where the line with parametric equations \(x = -12 + 3t,{\rm{ }}y = – 12 – 3t\) and \(z = 4 + 2t\) meets the \(YOZ\) plane.