4.01 Function notation
The point \left(7, - 6 \right) satisfies the function f(x). Write this using function notation.
If f \left(x\right) = 9 x^{2} + 7 x - 4, find:
f(-4)
f(10)
If f \left(x\right) = - 6 x + 4, find:
f \left( 4 \right)
f \left( 0 \right)
If f(x) = 4 x + 4, find:
f \left( 2 \right)
f \left( - 5 \right)
If f \left( x \right) = 3 x - 1, find:
f \left( 3 \right)
f \left( - 4 \right)
If g \left( x \right) = \dfrac{7 x}{4}, find:
g \left( 5 \right)
g \left( - 4 \right)
Consider the function f \left( x \right) = 4 + x^{3}.
Evaluate f \left( 4 \right)
Evaluate f \left( - 2 \right)
Consider the function f \left( x \right) = 2 x^{2} - 2 x + 5. Evaluate f\left(\dfrac{1}{2}\right).
Consider the function f \left( x \right) = \sqrt{ 5 x + 9}. Find the exact value of:
f \left( 0 \right)
f \left( 2 \right)
f \left( - 1 \right)
If f \left( t \right) = \dfrac{t^{3} + 27}{t^{2} + 9} , evaluate the following:
f \left( - 3 \right)
f \left( 3 \right)
f \left( 4 \right)
Consider the function f \left( x \right) = x^{2} + 8 x. Write an expression for:
f \left( a \right)
f \left( b \right)
Consider the function f \left( x \right) = 2 x^{3} + 3 x^{2} - 4.
Evaluate f \left( 0 \right).
Evaluate f \left( \dfrac{1}{4} \right).
If j(x) = 3^{x} - 3^{ - x }, find the following, rounding your answers to two decimal places if necessary:
j(0)
j(1)
j(4)
If m \left( x \right) = \sqrt{12^{2} - x^{2}}, find:
m \left( 4 \right)
m \left( 0 \right)
m \left( 9 \right)
m \left( \sqrt{2} \right)
Consider the function p \left( x \right) = x^{2} + 8.
Evaluate p \left( 2 \right).
Form an expression for p \left( m \right).
Consider the equation x + 3 y = 6.
Rewrite the equation using function notation f \left( x \right) for y.
Find the value of f \left( 3 \right).
Consider the equation x - 4 y = 8.
Rewrite the equation using function notation f \left( x \right).
Find the value of f \left( 12 \right).
Consider the equation y + 6 x^{2} = 3 - x.
Rewrite the equation using function notation f \left( x \right).
Find the value of f \left( 3 \right).
Consider the equation y - 4 x^{2} = 5 + x.
Rewrite the equation using function notation f \left( x \right).
Find the value of f \left( 2 \right).
Consider the equation - 6 x + 5 y = 7.
Rewrite the equation using function notation f \left( x \right).
Find the value of f \left( 3 \right).
Use the graph of the function f \left( x \right) to find each of the following values:
f \left( 0 \right)
f \left( - 2 \right)
The value of x such that f \left( x \right) = 3
Consider the relation h \left(x\right) = - x^{2} + 6 x - 6.
For any input value of x, state the maximum number of distinct output values h \left(x\right) can produce.
Is h \left(x\right) a function? Explain your answer.
For each of the following pairs of variables, determine which is the independent variable and which is the dependent variable:
Cost of pizza and size of pizza.
Mark achieved on a test and time spent studying.
Duration of a loan and amound borrowed.
Time spent exercising and physical fitness level.
Consider the function f(x) = x^{2} - 49.
Find:
f(1)
f(8)
f(0)
If f(x) = 12, what are the possible values for x, rounded to two decimal places?
Consider the function g \left( x \right) = a x^{3} - 3 x + 5.
Form an expression for g \left( k \right).
Form an expression for g \left( - k \right).
Is g \left( k \right) = g \left( - k \right)?
Is g \left( k \right) = - g \left( - k \right)?
If Z(y) = y^{2} + 12 y + 32, find y when Z(y) = - 3.
A function f \left( x \right) is defined by f \left( x \right) = \left(x + 4\right) \left(x^{2} - 4\right).
Evaluate f \left( 6 \right).
Find all solutions for which f \left( x \right) = 0.
A graph of a quadratic equation of the form y = a x^{2} + b x + c passes through the points \left(0, - 7 \right), \left( - 1 , - 8 \right) and \left(4, 77\right) .
Using the point \left(0, - 7 \right), find the value of c.
Substitute c and \left( - 1 , - 8 \right) into the equation y = a x^{2} + b x + c to obtain an equation that describes a in terms of b.
Substitute c and \left(4, 77\right) into the equation y = a x^{2} + b x + c to obtain a simplified second equation in terms of a and b.
Solve for a and b.