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maw [93]
3 years ago
10

The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 5 units,

the value of k is ________.

Mathematics
1 answer:
raketka [301]3 years ago
5 0
5. The value of k is the same of b in the original linear equation formula (y=mx+b). The b (or k here) changes where the equation itself fits on the graph. If a +0 is replaced with a -5, then the equation is shifted down by five units. I've graphed it below for you (where f(x) is in red and g(x) is in blue). Hope this helps!

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kolbaska11 [484]

Answer:

let common difference be d.

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2 years ago
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ohaa [14]

Answer:

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3 years ago
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jonny [76]

Answer:

0.5

Step-by-step explanation:

Ok, so it's asking for what (1/(x-1) - 2/(x^2-1)) approaches as x approaches 1. Before we deal with the limit, let's simplify the inside.

We want to combine the two fractions into one fraction. Therefore, we need a common denominator.

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the inside expression is therefore (x+1)/(x^2-1) - 2/(x^2-1)

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and that simplifies further to 1/(x+1).

Now this is a continuous function when x = 1, so to find the limit as x approaches 1 of this function, we can by definition just plug 1 in.

limx->1 (1/(x+1)) = 1/2.

The reason why we didn't just plug 1 in at the beginning is because the function wasn't continuous when x was 1.

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