Function

The number of integral solution $x$ of ${\log }_{\left(x+\frac{7}{2}\right)}{\left(\frac{x-7}{2x-3}\right)}^2\ge 0$ is

Solution of inequality

${\log }_{\sin x}\left({\log }_3\left({\log }_{0.2}\left(x\right)\right)\right)<0$ is

${\log }_{\left(x^2+1\right)}\left(5-x\right)$ is defined for all $x\in$

Solve $e^x=4x$ and find the number of slutions

Draw the graph of $y=e^x$

Draw the graph of $y=\sin \left(x\right)$.

Draw the graph, $y=e^x$

The exponential function $f\left(x\right)=e^x$ is a continuous function with domain $R$ and range 

The domain of $\left(2, 4\right), \left(3, 5\right), \left(4, 6\right), \left(5, 7\right)$ is _____.

$\sum _{n=1}^{\infty }\frac{2n^2+7n+5}{n!}$ is equal to

The diagram shows three graphs

$A$ is part of the line $y=x$. $B$ is part of the graph of $f\left(x\right)={\left(\frac{3}{2}\right)}^{x-1}+2$. $C$ is the reflection of $f\left(x\right)={\left(\frac{3}{2}\right)}^{x-1}+2$ in the line $y=x$. Write down the equation of the horizontal asymptote to the graph of $y=f\left(x\right)$.

A cup of tea is left on a table for several hours. The temperature of the tea in the cup is modelled by $T\left(t\right)=25+69e^{-0.143t}$, where $t$ represents the time in minutes that the cup of tea has been on the table. Write down the equation of the horizontal asymptote of the graph of $T$.

The value, $y$, of a car, in thousands of dollars, is modelled by the function $y=30{\left(0.9\right)}^x$, where $x$ is the number of years since the car was manufactured.

Use your GDC to estimate when the value of the car will be half of its original value.

The value, $y$, of a car, in thousands of dollars, is modelled by the function $y=30{\left(0.9\right)}^x$, where $x$ is the number of years since the car was manufactured.

Find the value of the car when it was new.

Consider the graph of the exponential function $f$ defined by $f\left(x\right)=16-4\times 2^{-x}$

State the domain of $f$

Teacher Tom makes a cup of coffee and leaves it on his table.

Its temperature $\left(H^{°}C\right)$ is modelled by the function $H=\left(65\right)2^{-\frac{t}{2}}+25,$ where $t$ is the tie in minutes after Tom makes the coffee.

Determine the temperature of the room where Tom set down his coffee.

Teacher Tom makes a cup of coffee and leaves it on his table.

Its temperature $\left(H^{°}C\right)$ is modelled by the function $H=\left(65\right)2^{-\frac{t}{2}}+25,$ where $t$ is the tie in minutes after Tom makes the coffee.

Find the temperature of the coffee after $3$ minutes.

Teacher Tom makes a cup of coffee and leaves it on his table.

Its temperature $\left(H^{°}C\right)$ is modelled by the function $H=\left(65\right)2^{-\frac{t}{2}}+25,$ where $t$ is the time in minutes after Tom makes the coffee.

State the initial temperature of the coffee.

The number of solutions of the equation ${\mathit{\text{a}}}^{\mathit{\text{f}}\left(\mathit{\text{x}}\right)}+\mathit{\text{g}}\left(\mathit{\text{x}}\right)=0$, where $a>0$, $\mathit{\text{g}}\left(\mathit{\text{x}}\right)\ne 0$ and has least value $\frac{1}{2}$ is