Function notation, domain and range Problem set B

\(g(x)=2x^2-7x+3\).

1. (a) Find \(g(4)\).
2. (b) Find \(g(-2)\).
3. (c) Find the values of x for which \(g(x)=3\).

Write down the largest possible domain of each function.

1. (a) \(p(x)=\dfrac{9}{x+2}\)
2. (b) \(q(x)=\sqrt{3x-12}\)
3. (c) \(r(x)=\ln(x+4)\)

Write down the range of each function, for all x in its domain.

1. (a) \(p(x)=(x+1)^2-5\)
2. (b) \(q(x)=-3x^2+12x-2\)
3. (c) \(r(x)=5^x-2\)

The graph shows \(y=g(x)\). The closed dot is at \((-1,\,5)\) and the open dot at \((5,\,5)\). Write down the domain and the range of g.

A taxi company charges \(F(k)=3.5+1.6k\) pounds for a journey of k kilometres.

1. (a) Find \(F(20)\).
2. (b) Find the length of a journey that costs £51.50.
3. (c) Say what \(F(0)\) means in this situation.

A parcel is dropped from a drone. Its height above the ground after t seconds is \(h(t)=125-5t^2\) metres. State a reasonable domain and range for the model.

A school has 80 m of edging for a rectangular flower bed. The width is x metres, so the area is \(A(x)=x(40-x)\) square metres. State a reasonable domain and range for the model.

Find the largest possible domain of \(f(x)=\dfrac{\sqrt{x+5}}{x-2}\), and the range of \(g(x)=\dfrac{6}{x+1}\), where \(x\neq-1\).

The function f is defined by \(f(x)=x^2-4x+1\) for \(0\leq x\leq6\). Find the range of f.