Which graph represents the function h(x) = -(x+6)³-3?
1 answer:
The correct answer is option B which is the second graph in the image showing the function h(x) = -(x+6)³-3.
<h3>What is a graph?</h3>A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
Given function:
h(x) = -(x+6)³-3.
The given function is cubic and cuts the x-axis at the point (-7.442,0) the graph is bending towards the left side in the second quadrant.
Therefore the correct answer is option B which is the second graph in the image showing the function h(x) = -(x+6)³-3.
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Let
A (1,6)------> location brianna's house on a map
B (5,3)------> location Jordan's house on a map
we know that
One possible path from brianna's house to jordan's house it's a straight line ( the shortest distance)
using a graph tool
see the attached figure
find the distance points AB
d=√[(y2-y1)²+(x2-x1)²]-----> d=√[(3-6)²+(5-1)²]----> d=√[3²+4²]d=√25----> d=25 units
the distance from brianna's house to jordan's house is 25 units
A (1,6)------> location brianna's house on a map
B (5,3)------> location Jordan's house on a map
we know that
One possible path from brianna's house to jordan's house it's a straight line ( the shortest distance)
using a graph tool
see the attached figure
find the distance points AB
d=√[(y2-y1)²+(x2-x1)²]-----> d=√[(3-6)²+(5-1)²]----> d=√[3²+4²]d=√25----> d=25 units
the distance from brianna's house to jordan's house is 25 units
The y-intercept of linear function (f- g)(x) is (0,9)
<h3>How to determine the y-intercept?</h3>The table of values is given as:
x -6 -4 -1 3 4
f(x) 15 11 5 -3 -5
g(x) -36 -26 -11 9 14
The equations of the functions is calculated using:
So, we have:
Evaluate
f(x) = -2x + 3
Also, we have:
Evaluate
g(x) = 5x - 6
Next, we calculate (f - g)(x) using:
(f - g)(x) = f(x) - g(x)
This gives
(f - g)(x) = -2x + 3 - 5x + 6
Substitute 0 for x
(f - g)(0) = -2(0) + 3 - 5(0) + 6
Evaluate
(f - g)(0) = 9
Hence, the y-intercept of (f- g)(x) is (0,9)
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