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3 years ago

1. What is the value of f(3) and what does it represent in the context of this example?

Mathematics

1 answer:

Marysya12 [62]3 years ago

3 0

Answer/step-by-step explanation:

The graph of f(x) above is said to be the quantity of liquid a cylinder holds when poured into it at a given time, x.

This means the quantity of the liquid poured in the cylinder is a function of time.

f(x) values (quantity of liquid) are plotted on the y-axis, while x values (time) are plotted on the x-axis.

f(3) is the value at the y-axis when x = 3. Thus, when x = 3, y = 6.

Therefore, the value of f(3) = 6

f(3) = 6, represents the quantity of liquid poured in the cylinder at 3 seconds.

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Given the the equation: y − 7 = x + 4 ;

We should rewrite the equation in "slope-intercept form" ; that is:

" y = mx + b " ;
______________________
in which: "y" remains an isolated variable on the "left-hand side" of the equation (with "no coefficients"—except the "implied coefficient of "1"
{since "1" , multiplied by any value, results in that same value} ;

"m" refers to the "slope" of the line;
and "m" is the coefficient of "x" ;

"b" refers to the "y-intercept" of the graphed (linear) equation; or more precisely, the value of "y" of the coordinate of the [ point on the graphed line of the equation—where the line crossed the "y-axis" ] ; that is; the "y-coordinate of the "y-intercept" ; that is, the value of "y" when "x = 0" ;
______________________________________________________
{Note that: "m" (the slope) may be a negative value; & that: "y" may be a negative value; as regard to the "slope-intercept form" equation:
that is:
"y = mx + b" . }.
______________________________________________________
So; given the equation:
______________________________________________________
" y − 7 = x + 4 " ;
______________________________________________________
Add "7" to each side of the equation;
to isolate "y" on one side of the equation;
→ {specifically, the "left-hand-side" of the equation} ;

and to rewrite the equation in "slope-intercept form" ; that is;
→ to rewrite the equation in the format:
" y = mx + b " ;
_______________________________________________________
As such: "y − 7 = x + 4 " ;
_______________________________________________________
→ Add "7" to each side of the equation:
_______________________________________________________
→ y − 7 + 7 = x + 4 + 7 ;

to get:
_______________________________________________________
  → y = x + 11 ;
_______________________________________________________
Now, let us graph the equation:
_______________________________________________________
Let us make a table:
_______________________________________________________
x ║ (x + 11) ║ y ║
_______________________________________________________
-20 ║ (-20 + 11) ║ -9 ║

-19 ║ (-19 + 11) ║ -8 ║

-18 ║ (-18 + 11) ║ -7 ║

-17 ║ (-17 + 11) ║ -6 ║

-16 ║ (-16 + 11) ║ -5 ║

-15 ║ (-15 + 11) ║ -4 ║

-14 ║ (-14 + 11) ║ -3 ║

-13 ║ (-13 + 11) ║ -2 ║

-12 ║ (-12 + 11) ║ -1 ║

-11 ║ (-11 + 11) ║ 0   ║

-10 ║ (-10+ 11) ║ 1 ║

-9 ║ (-9 + 11) ║ 2 ║

-8 ║ (-8 + 11) ║ 3 ║

-7 ║ (-7 + 11) ║ 4 ║

-6 ║ (-6 + 11) ║ 5 ║

-5 ║ (-5 + 11) ║ 6 ║

-4 ║ (-4 + 11) ║ 7 ║

-3 ║ (-3 + 11) ║ 8 ║

-2 ║ (-2 + 11) ║ 9 ║

-1 ║ (-1 + 11) ║ 10 ║

0 ║ (0 + 11) ║ 11 ║

1 ║ (1 + 11) ║ 12 ║

2 ║ (2 + 11) ║ 13 ║

3 ║ (3 + 11) ║ 14 ║

4 ║ (4 + 11) ║ 15 ║

5 ║ (5 + 11) ║ 16 ║
_________________________________________________

Now, we plot these points on a graph, and draw a line through these points; the slope is "1" ; since the equation is:
" y = x + 11 " ; Note: The slope, "m", is "1", since there is an "implied coefficient of "1" ; i.e. " y = 1x + 11 " .
___________________________________
Graph of: "y = x + 11 " ;
_____________________________________

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