A function is defined by
Find the value of
Write down the range of .
Find the value of .
Write down the range of the inverse function.
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A function is defined by
Find the value of
Write down the range of .
Find the value of .
Write down the range of the inverse function.
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Consider the function The domain of is
Find
Find the range of .
Write down the domain of the inverse function.
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Consider the function .
Sketch the graph of the function , labelling the and intercepts.
Find
Find
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Consider the functions and
Find the coordinates of the -intercepts for the graph of
Find the coordinates of the -intercepts for the graph of
For the graph of , find the equation of
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Consider the functions and .
Find the maximum possible domain and range of
For the graph of , find the equation of
Find the coordinates of the -intercepts for the graph of
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Consider the functions and .
Sketch the graphs of the functions and and label the coordinates of the vertices for both functions.
Find the coordinates for the points of intersection of and .
Find the -intercepts of and .
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The diagram below shows part of the graph of the function , where and are both integers. Points P(-2, 0) and R(6, 0) represent the -intercepts, point Q(0, 12) represents the -intercept, point V represents the vertex of the graph of and O represents the origin (0, 0).
Write down the value of .
Find the value of and write down
Write down the coordinates of .
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The function intercepts the -axis at , has an -intercept when and can be obtained by an appropriate translation of the graph .
Find the other -intercept of
Write down the coordinates of the vertex of .
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The diagram below shows the graph of the function for .
State the amplitude of .
Calculate the period of .
Find the possible values of when
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The diagram below shows part of the graph of the function
Points and represent where the graph of intersects the coordinate axes, write down the coordinates for
Points and represent the local maximum and minimum respectively for , write down the coordinates for
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The diagram below shows part of the graph of the function
Find
The point P represents the -intercept of Write down the coordinates of .
The point Q represents the -intercept of . Write down the coordinates of .
Draw the line on the graph above.
Write down the number of solutions to the equation
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Let . The diagram below shows part of the graph of .
Another function is defined by
Sketch the graph of on the axes above.
The graph of and intersect at points A and B.
Find the coordinates of A and B and label them on the diagram above.
Find the length of the line AB.
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Let , for .
For the graph of , find the:
For the graph of , write down the equation of any asymptotes.
Let for The graphs of and intersect at points and .
Write down the coordinates of P and Q.
Find the distance of .
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The perimeter, P, and area, A, of a given square can be expressed by and respectively, where is the length of the side of the square.
Write down an expression for:
Find the value of and .
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Consider the function where and are constants. The graph of passes through the points and and is shown below.
Write down two equations relating and .
Find the value of and .
Write down the equation of the horizontal asymptote of the graph of .
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The function intercepts the -axis at and has an -intercept at The function can be obtained by an appropriate shift of the graph .
Find the values of and .
Find the other -intercept of .
Determine the coordinates of the maximum value of .
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A function is defined by
Find the value of
For the graph of write down the equation of any asymptotes.
Find the range of .
The line intersects the graph of when and when
Find the equation of . Give your answer in the form , where and are integers.
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A function is defined by
Find the value of . Give your answer as a fraction.
Find the range of .
Find the value of . Give your answer as a fraction.
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The diagram below shows the graph of the function , for .
For the graph of , find the:
Write down the range of .
Three lines are drawn connecting the two local minimum points and the local maximum point forming a triangle. Calculate the area of the triangle.
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Let for
The th maximum point on the graph of has coordinate , where .
Given that , find and .
Using sigma notation, write down an expression for .
Find the value of the sum from part (b) (i). Give your answer to 2 decimal places.
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The average fat-free mass, M, in kg, of footballers as a function of their age, , in years, can be given by the logarithmic function:
Calculate the average fat free mass of players aged:
Find an expression for a linear model using your answers to part (a) (i) and (ii).
Calculate the percentage error from using the linear model found in part (b) to approximate the average fat free mass of a player aged 20 years old.
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The axes below shows the graph of the piecewise function,
The gradient of the graph of is 0 for .
Find the values of and .
Complete the following piecewise function for
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A function is defined by . The graph of has an axis of symmetry of
Find the value of .
Find the range of .
Another function is defined by . The graph of and intersect at points A and B.
Find the equation of the line passing through points A and B. Give your answer in the form
Find the distance of the line AB.
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Consider the function The line intersects the graph of at point A and B.
Find the value of and .
Find the equation of . Give your answer in the form , where and are fractions.
The line is the perpendicular bisector to [AB].
Find the equation of . Give your answer in the form , where and are integers.
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A rectangle has length and width .
Find an expression for
Show that .
The graph of the function P, for , is shown below.
On the grid above, draw the graph of the inverse function .
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The function is a quadratic in the form , for
The graph of has -intercepts and
Find the values of and
Another function can be defined by , for .
The graph of and intersect at points and .
Find the coordinates of and .
Solve the inequality .
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Let for
The th minimum point on the graph of has coordinate , where .
Given that , find .
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Let where .
Solve the inequality .
For the graph of , find the coordinates of the
Write down the possible domains of for which has an inverse and explain why the domain must be restricted.
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The graph of a quadratic function has equation , where and the axis of symmetry is .
Draw the axis of symmetry on the grid above.
The graph of the quadratic function intersects the -axis at points and B.
Write down the coordinates of B.
Find the values of and .
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The diagram below shows part of the graph of the function , where points A, B, C and D represent stationary points. The points A, B, C and D are joined together forming a quadrilateral ABDC.
Write down the coordinates for
Find the area of the quadrilateral ABDC.
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The intensity of light, I, is assumed to be 100% at the surface of the ocean and decreases with depth, , and can be estimated by the function
where is expressed as a percentage, is the depth below the surface, in metres, and is a constant.
Calculate the value of .
State the domain and range of .
On a particularly bright day the intensity of light 6.2 m below the surface is 75%.
Calculate the percentage error between the estimate made by the function and the actual intensity of light.
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Graph the following piecewise function on the grid below
Find the values of when
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