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faust18 [17]
3 years ago
6

Which of the following statements are true? Select all that apply.

Mathematics
1 answer:
gulaghasi [49]3 years ago
6 0

Answer:

  • Both functions have the same slope.
  • The origin is the y-intercept for the function expressed in the table.
  • The table and the graph express an equivalent function.

Step-by-step explanation:

Both functions have the same slope

The slope is m in the equation; y =mx+c which is the formula for a straight line.

m = change in Y/change in x

Using 2 points: (1,3/4) and ( 4,3) from the table;

= (3 - 3/4) / ( 4 - 1)

= 2.25/3

= 0.75 which is 3/4 which is the same as the slope of the function in the equation.

The origin is the y-intercept for the function expressed in the table.

Slope of function in table is known to be 0.75. Find c to complete equation.

3 = 0.75 ( 4) + c

3 = 3 + c

c = 0

c is the y-intercept. The origin of a line is 0 so if c is 0 then the origin is the y intercept.

The table and the graph express an equivalent function.

The function for the table as calculated is;

y = 0.75x + 0

y = 0.75x

This is the same as the function for the equation for the graph which is y = 3/4x.

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Answer:

For f(x+\frac{5}{4}), f(x) is translated \frac{5}{4} units left.

For f(x)-\frac{5}{4}, f(x) is translated \frac{5}{4} units down.

Step-by-step explanation:

The transformation of f(x)\rightarrow f(x+C) means that the graph shift to left by C units if C is positive number and shifts to right by C units if C is a negative number.

The transformation of f(x)\rightarrow f(x)+C means that the graph shifts up by C units if C is positive number and shifts down by C units if C is a negative number.

Here, in the transformation of f(x)\rightarrow f(x+\frac{5}{4}),C = \frac{5}{4}>0, so, the function translates left by \frac{5}{4} units.

Similarly, in the transformation of f(x)\rightarrow f(x)-\frac{5}{4},C = -\frac{5}{4}, so, the function translates down by \frac{5}{4} units.

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3 years ago
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Answer:

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Step-by-step explanation:

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Simplify (5 +1)2 — (12 + 32) + 3
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Step-by-step explanation:

=( 5 + 1 )2 - ( 12 + 32 ) + 3

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Answer:

x^2+7x-8-\frac{3}{x-7}

Step-by-step explanation:

I think this question is a bit hard to explain by typing, so I'll add an image down below.  

I used long division for this question, and the final answer is: x^2+7x-8-\frac{3}{x-7}

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