Which equation describes the graph shown?
- \(y=2 \cos ^{-1}(x+1)\)
- \(y= \sin ^{-1}(x-1)\)
- \(y=2 \cos ^{-1}(x-1)\)
- \(y=\dfrac{1}{2} \sin ^{-1}(x+1)\)
Aussie Maths & Science Teachers: Save your time with SmarterEd
Which equation describes the graph shown?
\(C\)
\(\text{Graph shape (general)}\ \ → \cos^{-1}(x) \)
\(\text{Graph translated 1 unit to the right}\ → \cos^{-1}(x-1) \)
\(\text{Range:}\ 0 \leq \cos^{-1}(x-1) \leq \pi\ \ →\ 0 \leq 2\cos^{-1}(x-1) \leq 2\pi \)
\(\Rightarrow C\)
The graph of the function `y = sin^(-1)(x-2)` is transformed by being dilated by a factor of 3 from the `y`-axis and then translated to the right by 2.
What is the equation of the transformed graph?
`A`
`y = sin^(-1)(x-2)`
`text(Dilate by factor 3 from the)\ ytext(-axis)`
`text(Swap:)\ \ x -> x/3`
`y_1` | `= sin^(-1)(x/3-2)` |
`= sin^(-1)((x-6)/3)` |
`text(Translate to the right by 2)`
`text(Swap:)\ \ x -> x-2`
`y_2` | `= sin^(-1)(((x-2)-6)/3)` |
`= sin^(-1)((x-8)/3)` |
`=>A`
The graph of the function `y = arccos(x-3)` is transformed by being dilated horizontally with a scale factor of `1/2` and then translated to the left by 1.
What is the equation of the transformed graph?
`C`
`y = cos^(-1)(x-3)`
`text(Dilate horizontally with scale factor)\ 1/2`
`text(Swap:)\ \ x -> 2x`
`y_1 = cos^(-1)(2x-3)`
`text(Translate to the left by 1)`
`text(Swap:)\ \ x -> x + 1`
`y_2` | `= cos^(-1)(2 (x + 1)-3)` |
`= cos^(-1)(2x + 2-3)` | |
`= cos^(-1)(2x-1)` |
`=>C`