Mathematics, 29.09.2019 22:30 earcake8692

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:
a. the function f(x) has a higher y-intercept.
b. the function g(x) has a higher y-intercept.
c. they both have the same y-intercept.
d. the relationship between y-intercepts cannot be determined

Answers: 2

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Answers

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

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.

b. The function g(x) has a higher y-intercept.

Answer from: jnaifuson

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

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

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)

$m=\frac{9-6}{7-4}$