Lesson test: The plane and the graph

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The plane and the graph

1.[2p]
What is the distance between $(- 4, 5)$ and $(8, - 11)$ ?

CorrectNot quite: 20

2.[2p]
What is the slope of the line through $(- 3, 11)$ and $(5, - 5)$ ?

CorrectNot quite: -2

3.[2p]
Give the equation of the line through $(2, 7)$ and $(6, 19)$ in the form y=mx+c, no spaces.

CorrectNot quite: y=3x+1

4.[2p]
A line has slope $3$ . What is the slope of any line perpendicular to it?

$- 1 / 3$

Correct

$1 / 3$

The answer is: $- 1 / 3$

$- 3$

The answer is: $- 1 / 3$

$3$

The answer is: $- 1 / 3$

5.[2p]
What does the vertical line test decide?

Whether a set of points is the graph of a function

Correct

Whether a function has an inverse

The answer is: Whether a set of points is the graph of a function

Whether a graph is symmetric

The answer is: Whether a set of points is the graph of a function

Whether a line is perpendicular to another

The answer is: Whether a set of points is the graph of a function

6.[3p]
Writing $y = 3 x^{2} + 12 x - 7$ in vertex form, what is the $y$ coordinate of the vertex?

CorrectNot quite: -19

7.[2p]
The graph of $y = f (x - 4)$ compared with the graph of $y = f (x)$ is

moved four units to the right

Correct

moved four units to the left

The answer is: moved four units to the right

moved four units down

The answer is: moved four units to the right

squeezed horizontally by a factor of four

The answer is: moved four units to the right

8.[1p]
The graph of $f^{- 1}$ is the reflection of the graph of $f$ in the line $y = x$ .

True

Correct

False

The answer is: True

9.[3p]
Match each feature of a graph to what it tells you about the function.

Crossings of the horizontal axis
A horizontal line meeting the curve twice
The set of heights the curve reaches
The turning point of a parabola

the vertex from completing the square
the function has no inverse
the solutions of $f (x) = 0$
the range

Show the answer

Crossings of the horizontal axis: the solutions of $f (x) = 0$ A horizontal line meeting the curve twice: the function has no inverse The set of heights the curve reaches: the range The turning point of a parabola: the vertex from completing the square

1.[2p] What is the distance between (−4,5) and (8,−11)?

2.[2p] What is the slope of the line through (−3,11) and (5,−5)?

3.[2p] Give the equation of the line through (2,7) and (6,19) in the form y=mx+c, no spaces.

4.[2p] A line has slope 3. What is the slope of any line perpendicular to it?

5.[2p] What does the vertical line test decide?

6.[3p] Writing y=3x2+12x−7 in vertex form, what is the y coordinate of the vertex?

7.[2p] The graph of y=f(x−4) compared with the graph of y=f(x) is

8.[1p] The graph of f−1 is the reflection of the graph of f in the line y=x.

9.[3p] Match each feature of a graph to what it tells you about the function.

1.[2p]
What is the distance between $(- 4, 5)$ and $(8, - 11)$ ?

2.[2p]
What is the slope of the line through $(- 3, 11)$ and $(5, - 5)$ ?

3.[2p]
Give the equation of the line through $(2, 7)$ and $(6, 19)$ in the form y=mx+c, no spaces.

4.[2p]
A line has slope $3$ . What is the slope of any line perpendicular to it?

5.[2p]
What does the vertical line test decide?

6.[3p]
Writing $y = 3 x^{2} + 12 x - 7$ in vertex form, what is the $y$ coordinate of the vertex?

7.[2p]
The graph of $y = f (x - 4)$ compared with the graph of $y = f (x)$ is

8.[1p]
The graph of $f^{- 1}$ is the reflection of the graph of $f$ in the line $y = x$ .

9.[3p]
Match each feature of a graph to what it tells you about the function.