Below are two different functions, f(x) and g(x). What can be determined about their y-intercepts?

f(x) = 4x − 1

chart:

x g(x)

1 3

4 6

7 9

Answer Choices:

AThe function f(x) has a higher y-intercept.
BThe function g(x) has a higher y-intercept.
CThey both have the same y-intercept.
DThe relationship between y-intercepts cannot be determined

For this case, the first thing to do is find the equation of the line for g (x).
We have then:
The equation of the line in point-slope form is given by:
\(y-yo = m (x-xo)\)
Where,
(xo, yo): point that belongs to the line
m: slope of the line
The slope is given by:
\(m = \frac{y2-y1}{x2-x1}\)
Substituting values:
\(m = \frac{6-3}{4-1}\)
Rewriting:
\(m = \frac{3}{3}\)
\(m=1\)
now we choose an ordered pair:
\((xo, yo) = (1, 3)\)
Substituting values we have:
\(y-3=(x-1)\)
We now rewrite the equation in its standard form:
\(y=x-1+3\)
\(y=x+2\)
Thus, the function g (x) is:
\(g(x)=x+2\)
On the other hand, the function f (x) is:
\(f(x)=4x-1\)
We note that the intersection with the y axis for g (x) is 2.
The intersection with the y axis for f (x) is -1.
Answer:
b. The function g(x) has a higher y-intercept.

ardni313 ardni313 · Answer 2 · 2019-09-10T23:48:39-04:00

It can be determined about their y-intercepts that b. The function g(x) has a higher y-intercept.

Further explanation

Straight-line equations are mathematical equations that are described in the plane of cartesian coordinates

General formula

\(\large{\boxed{\bold{y-y1=m(x-x1)}}}\)

or

y = mx + c

Where

m = straight-line gradient which is the slope of the line

x1, y1 = the Cartesian coordinate that is crossed by the line

c = constant

The formula for a gradient (m) between 2 points in a line

m = Δy / Δx

\(m=\frac{y_2-y_1}{x_2-x_1}\)

To find the equation of the line which has the point of intersection with the highest line of y then we enter the value of x in the equation = 0, so we know which value of y is greater

In the problem there is one known line equation (f (x)) and one line equation known for the value of x and its function (g (x))

For equation f (x) the value of the intersection with the y axis is: (x = 0)

f (x) = 4x - 1 (f (x) = y)

y = 4x - 1

y = 4.0 - 1

y = -1

For equation g (x), we first look for the equation by finding the gradient first

we specify the points: (4, 6) and (7, 9)

then the price gradient (m)

\(m=\frac{9-6}{7-4}\)

m = 3/3

m = 1

We enter in the general equation with point (4,6)

y-6 = 1 (x-4)

y-6 = x-4

y = x + 2

y = g (x) = x + 2

We enter the value x = 0 to get the value of the intersection with the y axis:

y = x + 2

y = 2

These two results show that: b. The function g (x) has a higher y-intercept.

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Keywords: function, y-intercept.