9514 1404 393
Answer:
f(x) = -1/2x +1
Step-by-step explanation:
The line crosses the y-axis at y=1, so the y-intercept is b=1.
The line drops 1 unit for a run of 2 to the right, so the slope is ...
m = rise/run = -1/2
The slope-intercept form of the equation of the line is ...
y = mx + b
y = -1/2x + 1
In functional form, the equation is ...
f(x) = -1/2x +1
Answer:
C. <em>c</em> is less than zero
Step-by-step explanation:
The parent radical function y=x^(1/n) has its point of inflection at the origin. The graph shows that point of inflection has been translated left and down.
<h3>Function transformation</h3>
The transformation of the parent function y=x^(1/n) into the function ...
f(x) = a(x +k)^(1/n) +c
represents the following transformations:
- vertical scaling by a factor of 'a'
- left shift by k units
- up shift by c units
<h3>Application</h3>
The location of the inflection point at (-3, -4) indicates it has been shifted left 3 units, and down 4 units. In the transformed function equation, this means ...
The graph says the value of c is less than zero.
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<em>Additional comment</em>
Apparently, the value of 'a' is 2, and the value of n is 3. The equation of the graph seems to be ...
f(x) = 2(x +3)^(1/3) -4
F(n)=3n
f(1/3)=3(1/3)
f(1/3)=1
Hope I didn't mess up for your sake
By "y = −9x2 − 2x" I assume you meant <span>y = −9x^2 − 2x (the "^" symbol represents exponentiation).
Let's find the first derivative of y with respect to x: dy/dx = -18x - 2. This is equivalent to the slope of the tangent line to the (parabolic) curve. Now let this derivative (slope) = 0 and solve for the critical value: -18x - 2 = 0, or
-18x = 2. Solving for x, x = -2/18, or x = -1/9.
When x = -1/9, y = -9(-1/9)^2 - 2(-1/9). This simplifies to y = -9/9 + 2/9, or
y = -7/9.
The only point at which the tangent to the curve is horiz. is (-1/9,-7/9).</span>
