Just by comparing the plots of f(x) and g(x), it's clear that g(x) is just some positive scalar multiple of f(x), so that for some constant k, we have
g(x) = k • f(x) = kx² = (√k x)²
The plot of the transformed function g(x) = (√k x)² passes through the point (1, 4), which means
g(1) = (√k • 1)² = 4
and it follows that k = 4. So g(x) = 4x² = (2x)² and B is the correct choice.
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The line's y-intercept is -3 as per the information given in the table.
<h3>What is meant by slope?</h3>
The slope or gradient of a line is a numerical representation of a line's steepness and direction in mathematics. The reason for this usage is unknown, but it first appears in English in O'Brien (1844), who wrote the equation for a straight line as y = mx + b, and in Todhunter (1888), who wrote it as y = mx + c. In this case, m stands for the line's slope.
Slope is the result of calculating the ratio of vertical change to horizontal change between (any) two distinct points on a line.
We know that,
y=m x +c
From the table the points are,
A(-2,5)
B(-1,1)
C(0,-3)
D(1,-7)
Substituting the C point in the above equation we get,
-3=m(0)+c
c=-3
Consequently, the line's y-intercept is -3.
To know more about slope, visit:
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Subtract 2 from each side of the equation, and
the answer will be right there, staring up at you.
Go ahead. It'll be very helpful for you.
Subtract the y-coordinates: -2 - 3 = -5
Subtract the x-coordinates in the same order: 1 - 1 = 0
slope = (difference in y)/(difference in x) = 5/0
Since the slope ends up as division by zero, and division by zero is undefined, the slope of this line is undefined.
Hint for future:
Vertical line: undefined slope
Horizontal line: zero slope
Line tilts up to the right: positive slope
Line tilts down to the right: negative slope