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cluponka [151]
3 years ago
15

Key Features of Graphs of Functions - Part 1

Mathematics
2 answers:
Vaselesa [24]3 years ago
6 0

Answer:

below

Step-by-step explanation:

Question 1:

In a function, every output value corresponds to exactly one input value.

The words that should be switched around are "output" and "input". This is because every input should have have only ONE output.

Question 2:

The following graph fails the vertical line test and is not a function. (YES)

Using the vertical line test to test whether the vertical line passes through the graphed function more then once. If it does, its not a function. If it doesn't, it is a function. Sadly, the vertical lines pass the point on two separate occasions which makes it not a function.

The vertical line shows gives the points (4, 2) and (4, -2).

Best of Luck!

dexar [7]3 years ago
5 0

Answer:

See below

Step-by-step explanation:

Q1.

  • In a function, every <u>output</u> value corresponds to exactly one <u>input </u>

value.

<em>The words to be interchanged are underlined. The function as per definition has exactly one output for each input.</em>

Q2.

Part A

  • Because it has 2 same input value for 2 different output values

Part B

  • The two points are (4, -2) and (4, 2)
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1. Write the standard form of the line that passes through the given points. (7, -3) and (4, -8)
Sveta_85 [38]

Answer:

1. -5x+3y+44=0

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Step-by-step explanation:

Standard form of a line is Ax+By+C=0.

If a line passing through two points then the equation of line is

y-y_1=m(x-x_1)

where, m is slope, i.e.,m=\dfrac{y_2-y_1}{x_2-x_1}.

1.

The line passes through the points (7,-3) and (4,-8). So, the equation of line is

y-(-3)=\dfrac{-8-(-3)}{4-7}(x-7)

y+3=\dfrac{-5}{-3}(x-7)

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3y+9=5x-35

-5x+3y+9+35=0

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Therefore, the required equation is -5x+3y+44=0.

2.

We need to find the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to 2 x + y =-5.

Slope of the line : m=\dfrac{-\text{Coefficient of x}}{\text{Coefficient of y}}=\dfrac{-2}{1}=-2

Slope of parallel lines are equal. So, the slope of required line is -2 and it passes through the point (0,2).

Equation of line is

y-2=-2(x-0)

y-2=-2x

2x+y-2=0

Therefore, the required equation is 2x+y-2=0.

3.

We need to find the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to 2x + y =-5.

From part 2, the slope of this line is -2. So, slope of required line is -2 and it passes through the point (2,0).

Equation of line is

y-0=-2(x-2)

y=-2x+4

2x+y-4=0

Therefore, the required equation is 2x+y-4=0.

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Step-by-step explanation:

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