Question

The functions f(x) and g(x) are described below: f(x) = 7x + 9 g(x) = 7x − 4 The graph of g(x) is obtained by shifting down the graph of f(x) by _____ units. Numerical Answers Expected!

Answer 1

Answer:

13

Step-by-step explanation:

The slope-intercept form of a line is given as:

$y=mx+c$

Where,

• m is the slope, and
• c is the y-intercept [the point in the axis where is cuts the y-axis]

So our first equation of $f(x)=7x+9$ has a y-axis cutting point at +9. The second equation of $g(x)=7x-4$ has a y-axis cutting point at -4. So, we can translate $f(x)$ 9 units to come down to $y=0$ and another more 4 units to come down to $y=-4$. In total we have to shift $f(x)$ 13 units down to get to $g(x)$.

The graphs of both the equations is shown in the attached picture for better understanding [ RED line is $f(x)$; BLUE line is $g(x)$]

Answer 2

The graph of each function is a sloping straight line, and

they both have the same slope (they're parallel).

In order to make the graph of  f(x)  coincide with (lie on top of) the

graph of  g(x),  you have to slide the graph of  f(x)  down  13 units.

You can look at their y-intercepts:  The intercept of  f(x) is  +9 ,

and the intercept of  g(x)  is  -4 .  So they cross the y-axis at

two points that are  13 units apart.  Since the lines are parallel,

they're  13 units apart everywhere. And the graph of g(x) is always the lower one.