Select the equivalent expression.
2 answers:
Answer:
Step-by-step explanation:
The given expression is:
Moving the expression to the other side in the fraction changes its sign to opposite. A numerator with negative exponent, when written in denominator will have the positive exponent. Using this rule, we can write:
The exponent 5 can be distributed to both numerator and denominator as shown:
The power of a power can be written as a product. i.e.
So, the expression similar to the given expression and with positive exponents is:
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Answer:
Or:
Step-by-step explanation:
We want to write the equation of a line that passes through the points (-6, 5) and (3, -5) in point-slope form.
Point-slope form is given by:
Thus, first, we need to find the slope. We can use the slope formula:
Next, we can use either of the two given points. I'll use (-6, 5). So, let (-6, 5) be (<em>x₁, y₁</em>). Substitute:
Or, fully simplified:
Using the other point, we will acquire:
Or, simplified:
a) The given function is
The domain refers to all values of x for which the function is defined.
The function is defined for
This implies that;
b) The vertical asymptotes are x-values that makes the function undefined.
To find the vertical asymptote, equate the denominator to zero and solve for x.
This implies that;
c) The roots are the x-intercepts of the graph.
To find the roots, we equate the function to zero and solve for x.
The roots are
d) The y-intercept is where the graph touches the y-axis.
To find the y-inter, we substitute;
into the function
e) to find the horizontal asypmtote, we take limit to infinity
The horizontal asymtote is
f) The greatest common divisor of both the numerator and the denominator is 1.
There is no common factor of the numerator and the denominator which is at least a linear factor.
Therefore the function has no holes.
g) The given function is a proper rational function.
There is no oblique asymptote.
See attachment for graph.
