smc-4422-35-Sketch graph

v1 Functions, 2ADV F1 2009 HSC 1a

Sketch the graph of \(y+\dfrac{x}{3} = 2\), showing the intercepts on both axes. (2 marks)

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\(y+\dfrac{x}{3} = 2\ \ \Rightarrow\ \ y=-\dfrac{1}{3}x+2\)

\(y\text{-intercept}\ = 2\)

\(\text{Find}\ x\ \text{when}\ y=0:\)

\(\dfrac{x}{3}=2\ \ \Rightarrow\ \ x=6\)

The graph of `y = 2x-3` will be drawn on this grid.

Which two points will the straight line pass through?

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`D`

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`text(Solution 1)`

`y = 2x-3\ text(passes through)\ (0, -3)`

`text(with a gradient of 2.)`

`:. A and C`

`text(Solution 2)`

`text{Substitute the coordinates of each point into the equation:}`

`A(-1, -5), \ B(1, -5), \ C(3, 3), \ D(-2, 1)`

`text(Only)\ A and C\ text(satisfy the equation) \ \ y = 2x-3.`

`=>D`

Which of the following is the graph of `y = 2x-2`?

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`D`

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♦ Mean mark 46%

`y = 2x-2`

`text(By elimination)`

`text(It has a)\ y\ text(intercept of)\ -2`

`=> text(Cannot be)\ B\ text(or)\ C`

`(-1, 0)text{ from}\ A\ text(doesn’t satisfy equation)`

`text(but)\ (1,0)\ text(from)\ D\ text(does)`

`=> D`

Sketch the graph of `y-2x = 3`, showing the intercepts on both axes. (2 marks)

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`y-2x=3\ \ =>\ \ y=2x+3`

`ytext{-intercept}\ = 3`

`text{Find}\ x\ text{when}\ y=0:`

`0-2x=3\ \ =>\ \ x=-3/2`