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Whitepunk [10]
3 years ago
8

Which of the following has a graph that is a straight line?

Mathematics
2 answers:
Amiraneli [1.4K]3 years ago
5 0
y = 2x + 7 because it's a linear function.
Jet001 [13]3 years ago
5 0

Answer:

Equation 1: y = 2x + 7

Step-by-step explanation:

In general the equation of a straight line is:

y=mx+c where m is the slope of the line and c is the y intercept

Or we can say that a graph is a straight line if it is a linear function.

Equation 1: y = 2x + 7

It is a linear function hence, its graph is a straight line

Equation 2: y² = x − 1

 It is not a linear function hence, its graph is not a straight line

Equation 3: y = 2x² + 4

 It is not a linear function hence, its graph is not a straight line

Equation 4: y = 3x³

It is not a linear function hence, its graph is not a straight line

Hence, The equation whose graph is a straight line is:

Equation 1: y = 2x + 7

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6 0
4 years ago
Use the power series for 1 1−x to find a power series representation of f(x) = ln(1−x). What is the radius of convergence? (Note
Viktor [21]

a. Recall that

\displaystyle\int\frac{\mathrm dx}{1-x}=-\ln|1-x|+C

For |x|, we have

\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n

By integrating both sides, we get

\displaystyle-\ln(1-x)=C+\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}

If x=0, then

\displaystyle-\ln1=C+\sum_{n=0}^\infty\frac{0^{n+1}}{n+1}\implies 0=C+0\implies C=0

so that

\displaystyle\ln(1-x)=-\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}

We can shift the index to simplify the sum slightly.

\displaystyle\ln(1-x)=-\sum_{n=1}^\infty\frac{x^n}n

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\displaystyle x\ln(1-x)=-\sum_{n=1}^\infty\frac{x^{n+1}}n

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4 0
3 years ago
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