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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

State the domain and range of \(y = \sqrt {1 – x} + 2\).

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Incorrect

Question 3 of 10

3. 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 \(a + b + c + d\).

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

Correct

Incorrect

Hint

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

Question 4 of 10

4. Question

Find all values of \(k\) for which \({x^2} – 2x + k = 0\) has a repeated root.

Correct

Incorrect

Hint

\(\begin{align} \displaystyle {b^2} – 4ac &\gt 0 \text{ two real solutions }\\ {b^2} – 4ac &= 0 \text{ one real solution }\\ {b^2} – 4ac &\lt 0 \text{ no real solutions } \end{align}\)

Question 5 of 10

5. Question

Find the maximum or minimum value of \(y = {x^2} – 4\), and the corresponding value of \(x\).