Answer:
f(x) approaches positive infinity.
g(x) approaches negative infinity.
the y-intercept of f(x) is less than the y-intercept of g(x).
Step-by-step explanation:
the highest power of x in f(x) is 3, and it has a positive sign. so, the bigger x the more the x³ part will dominate.
therefore, with x going to positive infinity, also f(x) goes to positive infinity.
the graph of g(x) clearly dives down never to come back up or flatten out. so, with x going to positive infinity, g(x) goes to negative infinity.
the y-intercept of f(x) = f(0).
that means the functional value when x=0.
so, for x=0 this means
y = 2×0³ - 3×0² + 5×0 + 7 = 7
the graph of g(x) shows that g(0) is 8.
so f(0) is less than g(0).
Answer:
7/2
Step-by-step explanation:
The slope of the line is given by
m = (y2-y1)/(x2-x1)
= (12-5)/(3-1)
= 7/2
Answer:
left 1 unit, up 5 units
Step-by-step explanation:
To answer the question:
<em>Which translation maps the graph of the function f(x) = x² onto the function g(x) = x² + 2x + 6?</em>
we need to find the vertex of g(x), as follows:
- x-coordinate of the vertex (h): -b/(2a) = -2/(2*1) = -1
- y-coordinate of the vertex (k): y = (-1)² + 2(-1) + 6 = 5
Therefore, g(x) can be rewritten as:
g(x) = a(x - h)² + k
g(x) = (x + 1)² + 5
which is the equation of f(x) = x² translated 1 unit to the left and 5 units up.
The equation of a circle is given in the form
, where
(a, b) is the centre of the circle
r = radius
We have the centre of the circle (-27, 120)
We can work out the radius by modelling the radius as the hypotenuse of a triangle as shown in the diagram below
The equation of the circle is
![[x-(-27)]^2+[y-120]^2=15129](https://tex.z-dn.net/?f=%5Bx-%28-27%29%5D%5E2%2B%5By-120%5D%5E2%3D15129)
![[x+27]^2+[y-120]^2=15129](https://tex.z-dn.net/?f=%5Bx%2B27%5D%5E2%2B%5By-120%5D%5E2%3D15129)
Correct answer: option number 4
Y + 2 = -2(x - 5)
Simplify.
y + 2 = -2x + 10
Subtract 2 from both sides.
y = -2x + 10 - 2
Simplify.
y = -2x + 8 → Slope-intercept form
Our answer is the second option : y=-2x+8
~Hope I helped!~
