f(5) = 3 means (5,3) is on the graph of f.
On the new graph, y = f(x+1) + 2, what do the +1 and +2 do?
Things inside the function notation inpact the x-values, since that's where x sits.
This outside the f(x) notation impact the y-values, since those are done after you've evaluated the function.
"+1" on the inside shifts every point to the left 1 unit. (Inside changes are almost always opposite from what it looks like it would do.)
"+2" on the outside will shift every point up by 2 units.
So what do you get if you take (5,3) and shift it left 1 and up 2?
A vertical stretch of scale factor 2, followed by a translation of 4 units left and 1 unit down is written as:
g(x) = 2*f(x + 4) - 1
<h3>
How to write the given transformation?</h3>
For a general function f(x), a vertical stretch of scale factor K is written as:
g(x) = K*f(x).
<u><em>Horizontal translation:</em></u>
For a general function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N).
- If N is positive, the shift is to the left.
- If N is negative, the shift is to the right.
<u><em>Vertical translation:</em></u>
For a general function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N.
- If N is positive, the shift is upwards.
- If N is negative, the shift is downwards.
So, if we start with a function f(x) and we stretch it vertically with a scale factor of 2, we get:
g(x) = 2*f(x)
Then we translate it 4 units left:
g(x) = 2*f(x + 4)
Then we translate 1 unit down:
g(x) = 2*f(x + 4) - 1
This is the equation for the transformation.
If you want to learn more about transformations, you can read:
brainly.com/question/4289712
Answer:
Step-by-step explanation:
x
y
−
4
0
−
3
1
−
3
−
1
−
2
2
−
2
−
2
The surface area of the box is <u>1048 square inches</u>
<h3>How to calculate the total surface area of the box</h3>
The formula for calculating the surface area of the prism is expressed as:
Surface area = 2(lw + wh +lh)
Given the following
l = 20in
w = 8in
h = 13in
Substitute the given parameters'
Surface area = 2(lw + wh +lh)
Surface area = 2(20(8) + 8(13) +20(13))
Surface area = 2(160+104+260)
Surface area = 1048 square inches
Hence surface area of the box is <u>1048 square inches</u>
Learn more on surface area of box here: brainly.com/question/26161002
I think you mean 8x^2 + 7 =0
a = 8 b = 0 c = 7
x= [-b +- square root (b^2 - 4*a*c)] / 2a
x = [0 +- square root (0 - 4*8*7)] / 2*8
x = +- square root (-224) / 16
x = +-
<span>
<span>
<span>
14.9666295471 * i
</span>
</span>
</span>
/ 16
x = +
<span>
<span>
<span>
0.9354143467
</span>
</span>
</span>
i
x = -
<span>
<span>
0.9354143467
</span>
</span>
i
