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

Question 3 of 10

3. Question

Determine whether \(f\left( x \right) = \dfrac{1}{{1 – 2{x^2}}}\) is odd, even or neither.

Correct

Incorrect

Question 4 of 10

4. Question

Find the vertical and horizontal asymptotes of \(y = \dfrac{{x – 2}}{{x – 1}}\).

\( vertical \ asymptote: \ x = \) \( horizontal \ asymptote: \ y = \)

Correct

Incorrect

Question 5 of 10

5. Question

If the domain of \(y = 2x – 1\) is \(1 \le x < 2\), state the range of \({y^{ - 1}}\).

Correct

Incorrect

Question 6 of 10

6. Question

Find the vertical asymptote(s) of \(f\left( x \right) = \dfrac{1}{{{x^2} + 4x + 3}}\).

Correct

Incorrect

Question 7 of 10

7. Question

Find the equation of the graph in red, where the graph of $y=e^x$ is given in blue.

Correct

Incorrect

Hint

$y=a^x$ is shifted to the right by $b$ units, $y=a^{x-b}$. $y=a^x$ is shifted to the left by $b$ units, $y=a^{x+b}$. $y=a^x$ is shifted up by $c$ units, $y=a^x + c$. $y=a^x$ is shifted down by $c$ units, $y=a^x – c$.

Question 8 of 10

8. Question

Express \({\log _b}108\) in terms of \(x,y\) or \(z\) , given \(x = {\log _b}2,y = {\log _b}3,z = {\log _b}5\).

The mass of radioactive \(t \) hours after establishment is \({R_t} = 800 \times {0.8^{0.5t}}\) grams. Find the time for the mass to reach 300 grams. Answer correct to the nearest minute.