Purchase this Material for $15

You need to sign up or log in to purchase.

Subscribe for All Access
You need to sign up or log in to purchase.

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`

Buy to View

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
```

Buy to View

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
```

Buy to View

0.49mins

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
```

Buy to View

2.04mins

Q2c

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

Buy to View

1.05mins

Q2d

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

Buy to View

1.29mins

Q2e

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

Buy to View

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.

Buy to View

1.09mins

Q3a

Buy to View

1.26mins

Q3b

Buy to View

1.29mins

Q3c

Buy to View

1.14mins

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
```

Buy to View

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
```

Buy to View

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
```

Buy to View

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)
```

Buy to View

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
```

Buy to View

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
```

Buy to View

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.

Buy to View

1.25mins

Q5a

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

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

to obtain each graph.

Buy to View

1.37mins

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

Buy to View

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

Buy to View

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

Buy to View

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

Buy to View

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

Buy to View

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

Buy to View

0.47mins

Q6f

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

Determine the equation of this transformed function.

Buy to View

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)`

.

Buy to View

2.52mins

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
```

Buy to View

0.34mins

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
```

Buy to View

0.18mins

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
```

Buy to View

0.32mins

Q9c

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

Buy to View

0.42mins

Q9d

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

Buy to View

0.30mins

Q9e

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

Buy to View

0.40mins

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.

Buy to View

0.17mins

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.

Buy to View

0.12mins

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.

Buy to View

0.50mins

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

Buy to View

0.36mins

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.

Buy to View

1.37mins

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?

Buy to View

0.35mins

Q14