Domain and Range of Functions

If $f\left(x\right)=\frac{x^2-x}{x^2+2x}$, then find the range of $f\left(x\right)$

If $f\left(x\right)=\alpha x+\beta$ and $f=\left\{\left(1,1\right),\left(2,3\right),\left(3,5\right),\left(4,7\right)\right\}$, then the values of $\alpha ,\beta$ are 

Consider the function $f\left(x\right)=x^2-x+1$ Find $f\left(0\right)+f\left(3\right)$.

The number of cells in a culture, $N,t$ hours after it has been established is shown in the graph for $0\le t\le 20$.

Estimate the interval of time over which the number of cells varied from $32$ to $64$.

The number of cells in a culture, $N,t$ hours after it has been established is shown in the graph for $0\le t\le 20$.

Estimate the value of $t$ when $N=32$.

The number of cells in a culture, $N,t$ hours after it has been established is shown in the graph for $0\le t\le 20$.

Estimate the value of $N$ when $t=4$.

The number of cells in a culture, $N,t$ hours after it has been established is shown in the graph for $0\le t\le 20$.

Estimate the initial number of cells in this culture.

The number of cells in a culture, $N,t$ hours after it has been established is shown in the graph for $0\le t\le 20$.

Find the range of this function.

The diagram shows the graph of a function $f$ from $A$ to $B$.

Write down the set $B$.

The diagram shows the graph of a function $f$ from $A$ to $B$.

Write down the set $A$.

The height, in metres, of a runner bean plant increases each week according to the formula $h\left(t\right)=0.25+\log 2t$, where $t$ is the time in weeks. Find the number of weeks it takes for the plant to reach a height of $2\text{m}$.

The height, in metres, of a runner bean plant increases each week according to the formula $h\left(t\right)=0.25+\log 2t$, where $t$ is the time in weeks. Find the height(in $\mathrm{m}$) of the plant after four weeks.(up to two decimals)  Use $\left(\log 8=0.90\right)$

The price of renting a car $(\pounds C)$ from "Cars-R-Us" for $d$ days is given by the formula $C=30+12.5d$.

The price of renting a car $(\pounds C)$ from "Car-nage" for $d$ days is given by the formula $C=70+8.35d$.

Abel wishes to rent a car for the duration of his holiday. He decides to rent from "Car-nage" as it will be cheaper for him. If Abel's holiday is between $14$ and $21$ days, find an inequality which shows the range in which Abel's car rental bill will lie.

 A function $f\left(x\right)$ is defined by $f\left(x\right)=3x-10$.

The range of function $f\left(x\right)$ is $5<f\left(x\right)<50$, find the domain of $f\left(x\right)$.

A function is given by $f\left(x\right)=128x-15$, $-3<x<15$.

Determine the value of $a$ such that $f\left(a\right)=1162.6$.

A function is given by $f\left(x\right)=128x-15$, $-3<x<15$.

Determine the range of the function $f$.

 A function is given by $f\left(x\right)=128x-15$, $-3<x<15$.

Determine the value of $f\left(\frac{3}{2}\right)$.

State the range of the following function.

State the domain of the following function.

State the range of the following function.