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Which graph best represents the equation y=x^2−2?
y=x2−2
y-intercept=−2 (when=0)
Quadratic is positive with vertex at y=−2
⇒ A
In 2004 there were 13.5 million registered motor vehicles in Australia. The number of registered motor vehicles is increasing at a rate of 2.3% per year.
Which expression represents the number (in millions) of registered motor vehicles, if y represents the number of years after 2004?
In 2004, 13.5 million
1 year later =13.5×(1.023)
2 years later =13.5×(1.023)×(1.023)
=13.5×(1.023)2
∴y years later =13.5×(1.023)y
⇒ A
Which graph best represents y=3^x?
y=3^x passes through (0,1)
and is exponential
⇒ D
The diagram shows the graph of an equation.
Which of the following equations does the graph best represent?
Graph is a parabola that passes
through (0,1)
⇒ C
Which of the following graphs best represents the equation y = a^x, where a is a positive number greater than 1?
At x=0, y=1
As x↑, y↑ exponentially
⇒D
Leanne wants to build a rectangular vegetable garden in her backyard. She has 20 metres of fencing and will use a wall as one side of the garden. The plan for her garden is shown, where x metres is the width of her garden.
Which equation gives the area, A, of the vegetable garden?
Length of garden=(20−2x)
Area =x(20−2x)
=20x−2×2
⇒ D