smc-830-10-Identify Graphs

v1 Algebra, STD2 A4 2021 HSC 10 MC

Which of the following best represents the graph of \(y = 5 (0.4)^{x}\) ?

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\(D\)

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\(\text{By elimination:}\)

♦ Mean mark 41%.

\(\text{When}\ x = 0, \ y = 5 \times (0.4)^0 = 5\)

\(\rightarrow\ \text{Eliminate B and C} \)

\(\text{As}\ \ x \rightarrow \infty, \ y \rightarrow 0 \)

\(\rightarrow\ \text{Eliminate A} \)

\(\Rightarrow D\)

v1 Algebra, STD2 A4 2008 HSC 4 MC

Which graph best represents \(y = \dfrac{2}{x}\) ?

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\(B\)

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\(y = \dfrac{2}{x}\ \text{does not touch either axis (inverse graph)}.\)

\(\Rightarrow B\)

v1 Algebra, STD2 A4 2018 HSC 4 MC

Which graph best represents the equation \(y = 2-x^2\) ?

A.		B.
C.		D.

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\(D\)

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\(y = 2-x^2\)

\(y\text{-intercept}\ = -2\ \ \text{(when}\ x = 0)\)

\(\text{Quadratic is concave down (sad) with vertex at}\ (0,2). \)

\(\Rightarrow A\)

Algebra, STD2 A4 2021 HSC 10 MC

Which of the following best represents the graph of `y = 10 (0.8)^x`?

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`A`

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`\text{By elimination:}`

♦ Mean mark 41%.

`\text{When} \ x = 0 \ , \ y = 10(0.8) ^0 = 10`

`-> \ text{Eliminate B and D}`

`text(As)\ \ x→oo, \ y→0`

`-> \ text{Eliminate C}`

`=> A`

Algebra, STD2 A4 2020 HSC 1 MC

Which of the following could represent the graph of `y = -x^2 + 1`?

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`C`

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♦ Mean mark 53%.
COMMENT: A surprisingly low State mean mark!

`=> C`

Algebra, STD2 A4 SM-Bank 3 MC

Which graph best represents the equation `y = 5^(−x)`?

A.		B.
C.		D.

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`D`

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`y`	`= 5^(−x)`
	`= 1/(5^x)`

`text(At)\ \ x = 0, \ y = 1`

`text(As)\ \ x -> ∞, \ y -> 0`

`=> D`

Algebra, STD2 A4 SM-Bank 1 MC

The graph below represents `y = a^x`.

What is the approximate value of `2(a^5)`?

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`B`

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`text(From graph:)`

`a^5`	`=4`
`:. 2(a^5)`	`= 2 xx 4`
	`= 8`

`=>\ text(B)`

Algebra, STD2 A4 2018 HSC 4 MC

Which graph best represents the equation `y = x^2-2`?

A.		B.
C.		D.

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`A`

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`y = x^2-2`

`ytext(-intercept) = -2\ \ \ (text(when) = 0)`

`text(Quadratic is positive with vertex at)\ \ y = -2`

`=>A`

Algebra, STD2 A4 2008 HSC 4 MC

Which graph best represents `y = 3^x`?

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`D`

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`y = 3^x\ \ text(passes through)\ \ (0,1)\ \text(and is exponential.)`

`=> D`

Algebra, STD2 A4 2014 HSC 3 MC

The diagram shows the graph of an equation.

Which of the following equations does the graph best represent?

`y = 3/x + 1`
`y = 3^x + 1`
`y = 3x^2 + 1`
`y = 3x^3 + 1`

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`C`

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`text(Graph is a parabola that passes through)\ (0, 1).`

`=> C`

Algebra, STD2 A4 2011 HSC 6 MC

Which of the following graphs best represents the equation `y = a^x`, where `a` is a positive number greater than 1?

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`D`

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♦ Mean mark 48%

`text(At) \ x=0,\ y=1`

`text(As)\ x uarr, \ \ y ↑\ text(exponentially)`

`=>D`