The graph of g(x) is the graph of f(x)=x+9 reflected across the y-axis.
2 answers:
Answer:
g(x) = -x +9
Step-by-step explanation:
Reflecting across the y-axis involves changing the sign of x, so the reflection of f(x) is ...
... g(x) = f(-x) = (-x) +9
The appropriate choice is ...
... g(x) = -x+9
<h2>Answer:</h2>
The equation which describes the function g is:
The graph of the function f(x) is given by:
Now, we know that the transformation of the function f(x) when the graph is shifted across the y-axis then it is given by:
f(x) → f(-x)
This means that:
g(x)=f(-x)
i.e.
g(x)= -x+9
Hence, the equation which will represent the graph of the function g(x) is given by:
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Answer: 1 : 3
Shaded area:
Unshaded area:
Ratio of shaded to unshaded:
Isolate the term with .
Differentiate both sides with respect to .
By the product and chain rules,
Solve for the partial derivative, then evaluate at .
Answer:
y = 2(x - 1/4)
Step-by-step explanation:
To find an equation of the tangent to a given curve, we need two vital information; one is the slope of the tangent (SOP) and the other is the point of tangency (POT).
to find the slope of tangent i will use the implicit differentiation to find the slope then apply the point given
so, first, the slope using implicit differentiation;
f(x) =
f'(x) = {tex}2x + 2y dy/dx = 2(3x^{2} + 4y^{2} - x)(6x + 8y dy/dx - 1){/tex}
applying the co-ordinates given; x = 0 and y = 1/4
SOP 2(0) + 2(1/4) dy/dx = 2[3(0)^2 + 4(1/4)^2 - 0][6(0) + 8(1/4) dy/dx - 1)
1/2 dy/dx = 2[4(1/16)][(8/4) dy/dx - 1]
1/2 dy/dx = 2[1/2][2 dy/dx - 1]
1/2 dy/dx = 2 dy/dx - 1
putting the dy/dx together
1 = 2 dy/dx - 1/2 dy/dx
1 = dy/dx (2 - 1/2)
make dy/dx subject
1 / 1/2 = dy/dx
therefore SOP = 2
POT
f(x) = (0)^2 + (1/4)^2 = [3(0)^2 + 4(1/4)^2 - 0]^2
1/16 = [4(1/16)]^2
1/16 = (1/4)^2
1/16 = 1/16
y = 0
using the slope formula
m = y - y2/ x - x2
2 = y - 0/ x - 1/4
y = 2(x - 1/4)