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.
__
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) → ∞
_____
<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:
A) 0.265
B) 0.0265
C) 0.837
D) 0.0837
E) 0.00265
F) 0.00837
Step-by-step explanation:
We are given;
√7 = 2.65 and √70 = 8.37
A) √0.07 can be rewritten as;
√(7 × 1/100)
Let's deal with the digits in the bracket.
Square root of 100 is 10. Thus;
√(7 × 1/100) = (1/10)√7 = (1/10) × 2.65 = 0.265
B) √0.0007
Rewrite to get;
√(7 × 1/10000)
Square root of 1/10000 is 1/100
Thus;
√(7 × 1/10000) = (1/100)√7 = (1/100) × 2.65 = 0.0265
C) √0.7
Like above;
√0.7 = √(70 × (1/100))
>> (1/10)√70 = (1/10) × 8.37 = 0.837
D) √0.007
Like above;
Rewrite to get;
√(70 × 1/10000)
Square root of 1/10000 is 1/100
Thus;
√(70 × 1/10000) = (1/100)√70 = (1/100) × 8.37 = 0.0837
E) √0.000007
Rewritten to;
√(7 × (1/1000000))
√(1/1000000) = 1/1000
Thus; √(7 × (1/1000000)) = 1/1000 × √7 = 1/1000 × 2.65 = 0.00265
F)√0.00007
Rewritten to;
√(70 × (1/1000000))
√(1/1000000) = 1/1000
Thus; √(70 × (1/1000000)) = 1/1000 × √70 = 1/1000 × 8.37 = 0.00837
Answer:
La división de dos números enteros es igual al valor absoluto del cociente de los valores absolutos entre el dividendo y el divisor, y tiene de signo, el que se obtiene de la aplicación de la regla de los signos.