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Solutions
40 Videos

Match each equation with the most suitable graph.

- (a)
`f(x) = 2(x + 1)^2 + 1`

- (b)
`g(x) = -\frac{1}{3}(x +1)^3 - 1`

- (c)
`y = 0.2(x -4)^4 -3`

- (d)
`y = -1.5(x + 3)^4 +4`

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0.31mins

Q1

State the parent function that must be transformed to create the graph of each of the following functions. Then describe the transformations that must be applied to the parent function.

```
\displaystyle
f(x) =\frac{5}{4}x^4 +3
```

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1.42mins

Q2a

State the parent function that must be transformed to create the graph of each of the following functions. Then describe the transformations that must be applied to the parent function.

```
\displaystyle
g(x) = 3x -4
```

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Q2b

State the parent function that must be transformed to create the graph of each of the following functions. Then describe the transformations that must be applied to the parent function.

```
\displaystyle
y = (3x +4)^3 - 7
```

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Q2c

```
\displaystyle
y = -(x + 8)^4
```

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Q2d

```
\displaystyle
y = -4.8(x - 3)(x -3)
```

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1.29mins

Q2e

```
\displaystyle
y = 2(\frac{1}{5}x + 7)^3 -4
```

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1.57mins

Q2f

Describe the transformations that were applied to the parent function to create each of the following graphs. Then write the equation of the transformed function.

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Q3a

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1.26mins

Q3b

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1.29mins

Q3c

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Q3d

Describe the transformations that were applied to `y = x^3`

to create
each of the following functions.

```
\displaystyle
y = 12(x - 9)^3 - 7
```

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0.54mins

Q4a

Describe the transformations that were applied to `y = x^3`

to create
each of the following functions.

```
\displaystyle
y = (\frac{7}{8}(x +1))^3 + 3
```

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1.30mins

Q4b

Describe the transformations that were applied to `y = x^3`

to create
each of the following functions.

```
\displaystyle
y = -2(x -6)^3 - 8
```

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1.13mins

Q4c

Describe the transformations that were applied to `y = x^3`

to create
each of the following functions.

```
\displaystyle
y = (x + 9)(x + 9)(x +9)
```

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0.37mins

Q4d

Describe the transformations that were applied to `y = x^3`

to create
each of the following functions.

```
\displaystyle
y = -2(-3(x - 4))^3 -5
```

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1.57mins

Q4e

Describe the transformations that were applied to `y = x^3`

to create
each of the following functions.

```
\displaystyle
y = (\frac{3}{4}(x -10))^3
```

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0.59mins

Q4f

For each graph, determine the equation of the function in the form `y = a(x - h)^2 + k`

. Then describe the transformations that were applied to `y = x^2`

to obtain each graph.

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Q5a

`y = a(x - h)^2 + k`

. Then describe the transformations that were applied to `y = x^2`

to obtain each graph.

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Q5b

The function `y = x^3`

has undergone the following sets of transformations. If `y= x^3`

passes through the points
`(-1, -1), (0, 0)`

, and `(2, 8)`

, list the coordinates of these transformed points on each new curve. Show your work.

vertically compressed by a factor of `\frac{1}{2}`

, horizontally compressed by `\frac{1}{5}`

a factor of 5, and horizontally translated 6 units to the left

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1.09mins

Q6a

The function `y = x^3`

has undergone the following sets of transformations. If `y= x^3`

passes through the points
`(21, 21), (0, 0)`

, and `(2, 8)`

, list the coordinates of these transformed points on each new curve.

reflected in the y-axis, horizontally stretched by a factor of 2, and vertically translated 3 units up

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0.49mins

Q6b

The function `y = x^3`

has undergone the following sets of transformations. If `y= x^3`

passes through the points
`(-2, -8), (0, 0)`

, and `(2, 8)`

, list the coordinates of these transformed points on each new curve.

reflected in the x-axis, vertically stretched by a factor of 3, horizontally translated 4 units to the right, and vertically translated `\frac{1}{2}`

of a unit down

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1.04mins

Q6c

The function `y = x^3`

has undergone the following sets of transformations. If `y= x^3`

passes through the points
`(21, 21), (0, 0)`

, and `(2, 8)`

, list the coordinates of these transformed points on each new curve.

vertically compressed by a factor of `\frac{1}{10}`

, horizontally stretched by a factor of 7, and vertically translated 2 units down

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0.48mins

Q6d

The function `y = x^3`

has undergone the following sets of transformations. If `y= x^3`

passes through the points
`(21, 21), (0, 0)`

, and `(2, 8)`

, list the coordinates of these transformed points on each new curve.

reflected in the y-axis, reflected in the x-axis, and vertically translated `\frac{9}{10}`

of a unit up

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0.49mins

Q6e

`y = x^3`

has undergone the following sets of transformations. If `y= x^3`

passes through the points
`(21, 21), (0, 0)`

, and `(2, 8)`

, list the coordinates of these transformed points on each new curve.

horizontally stretched by a factor of 7, horizontally translated 4 units to the left, and vertically translated 2 units down

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0.47mins

Q6f

The graph shown is a result of transformations applied to `y = x^4`

Determine the equation of this transformed function.

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1.19mins

Q7

Dillan has reflected the function `g(x) = x^3`

in the x-axis, vertically A compressed it by a factor of `\displaystyle \frac{2}{3}`

, horizontally translated it 13 units to the right, and vertically translated it 13 units down. Three points on the resulting curve are `\displaystyle(11, -\frac{23}{3})`

, `(13, -13)`

, and `\displaystyle(15, -\frac{55}{3})`

.

Determine the original coordinates of these three points on `g(x)`

.

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Q8

Determine the x-intercepts of each of the following polynomial functions. Round to two decimal places, if necessary.

```
\displaystyle
y = 2(x +3)^4 -2
```

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Q9a

Determine the x-intercepts of each of the following polynomial functions. Round to two decimal places, if necessary.

```
\displaystyle
y = (x -2)^3 - 8
```

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Q9b

Determine the x-intercepts of each of the following polynomial functions. Round to two decimal places, if necessary.

```
\displaystyle
y = -3(x + 1)^3 + 48
```

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Q9c

```
\displaystyle
y = -5(x + 6)^4 -10
```

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Q9d

```
\displaystyle
y = 4(x - 8)^4 -12
```

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Q9e

```
\displaystyle
y = -2(2x + 5)^3 - 20
```

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Q9f

Consider the function `y = 2(x - 4)^n + 1, n \in \mathbb{N}`

.

How many zeros will the function have if n = 3? Explain how you know.

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Q10a

Consider the function `y = 2(x - 4)^n + 1, n \in \mathbb{N}`

.

How many zeros will the function have if n = 4? Explain how you know.

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Q10b

For what values of `n`

will the reflection of the function `y = x^n`

in the x-axis be the same as its reflection in the y-axis. Explain your reasoning.

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Q11a

For what values of `n`

will the reflection of the function `y = x^n`

in the x-axis be the same as its reflection in the y-axis. Explain your reasoning.

For what values of `n`

will the reflections be different? Explain your

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Q11b

What transformations are required on the function `y = (x- 4)(x + 1)(x - 8)`

to create the function `y = 2(x -1)(x + 4)(x - 5)`

? Show your work.

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Q13

The function `f(x) = x^2`

was transformed by vertically stretching it, horizontally compressing it, horizontally translating it, and vertically translating it. The resulting function was then transformed again by reflecting it in the x-axis, vertically compressing it by a factor of `\frac{4}{5}`

, horizontally compressing it by a factor of `\frac{1}{2}`

, and vertically
translating it 6 units down. The equation of the final function is
`f(x) = -4(4(x + 3))^2 - 5`

. What was the equation of the function after it was transformed the first time?

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Q14

Lectures
5 Videos