Determine the intercepts of the line. -5x+9y=-18
1 answer:
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9514 1404 393
Answer:
D: all real numbers
R: f(x) > 0
A: f(x) = 0
(-∞, 0), (+∞, +∞)
vertical stretch by a factor of 2; left shift 2 units
Step-by-step explanation:
The transformation ...
g(x) = a·f(b(x -c)) +d
does the following:
- vertical stretch by a factor of 'a'
- horizontal compression by a factor of 'b'
- translation right by 'c' units
- translation up by 'd' units
For many functions, horizontal coordinate changes are indistinguishable from vertical coordinate changes. Exponential functions tend to be one of those.
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Using the above notation, you seem to have f(x) = 3^x, and g(x) = 2f(x+2). The transformation is a vertical stretch by a factor of 2, and a translation left 2 units.
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As with all exponential functions, ...
- the domain is "all real numbers"
- the range is all numbers above the asymptote: f(x) > 0
- the horizontal asymptote is f(x) = 0
The function is a growth function, so ...
- x → -∞, f(x) → 0
- x → ∞, f(x) → ∞
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<em>Additional comment</em>
The left shift is equivalent to an additional vertical stretch. The function could be rewritten as ...
f(x) = 18(3^x)
with no left shift and a vertical stretch by a factor of 18 instead of 2.
Answer:
Step-by-step explanation:
We have a circle that is split in three sections, two of which we know and we are asked to find the third missing section.
For the circle, we know that 4/5 and 1/10 is fit. Now we need the last one, to solve, we need to get the same denominator and see how much is missing.
Since 1/10 is our highest denominator, let's change 4/5 to have 10 as a denominator. Which would be through multiplying 5 to get 10.
What times 5 equals 10?
2
Now multiply both numerator and denominator by 2 to get our portion.
Now we have the same denominator, let's add our two fractions and see how much we have left.
8/10 + 1/10
9/10
We have 1/10 missing, therefore 1/10 is the answer.