Which of the following, to the nearest tenth, is a solution of f(x) = g (x) if f (x) = in (x + 5 ) - 1 and g(x) =x^3 - 2x+1
1 answer:
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The graph of y=ax+b, where a≠0, is always a line:
i) increasing if a>0
ii) decreasing if a<0
Consider the decreasing case.
The line is above the x-axis, that is positive but decreasing. At 1 single point it cuts the x-axis, so x=0, and then it continues decreasing below the x-axis.
Back to our problem:
The graph of y=-1/2 x +2 is a decreasing line.,
so it CANNOT be
"positive over the interval (4, infinity) and negative over the interval (-infinity, 4)"
it is
"<span>negative over the interval (4, infinity) and positive over the interval (-infinity, 4)</span>"
the graph is "<span>positive over the interval (-infinity, 4)</span>", it means that the line is decreasing but above the x-axis until 4, (4 not included).
then, "negative over the interval (4, infinity)", which means that the line is now decreasing below the x-axis.
when x=4, the line cuts the x-axis.
check the graph of the line generated using desmos.com
So with these equations we need to find the y-intercept and the slope because:
y = mx+b
y = f(×)
b = y-intercept
m = slope (slope = rise/run, rise over run)
rise is y-axis
run is x-axis
The y-intercept is (0,-2)
So now we know that one of the answers must have -2 in it
b = -2
m= rise/run = -2/3
The answer is:
y = mx+b
y = f(×)
b = y-intercept
m = slope (slope = rise/run, rise over run)
rise is y-axis
run is x-axis
The y-intercept is (0,-2)
So now we know that one of the answers must have -2 in it
b = -2
m= rise/run = -2/3
The answer is:
Slope is 3