Question

HELP HELP HELP ME SOMEONE PLSSSSSS PLSSS

Answer 1

Step-by-step explanation:

For g(x) = f(x) + 5:

Because f(x) = x, this can be simplified to:

y = x + 5

For h(x) = 2 * f(x) - 3, simplified to:

2*x - 3 or 2x - 3

For j(x) = $\frac{1}{2} * f(x) - 1$, simplified it is

$\frac{1}{2}x - 1$

For f(x), this can be drawn relatively easy, it is a linear line starting at the coordinates (0,5) gradually increasing by 1 in both the y and x axis. It can be drawn parallel to the line given in your question just one above.

For h(x), the line will start at (0, -3) but then have an incline of 2, i.e. the second point would be at 1, -1, and the third at (3, 3). This is because you are doubling the value of x but subtracting 3.

For j(x), x is halved so the line will be less steep although it will start at the coordinate (0, -1) because 1 is being subtracted.

Hope this helps!

Answer 2

Answer:

This is only for the first part. Please see the attached image for the graphs of the three given functions.

Step-by-step explanation:

1. g(x) = f(x) + 5

This involves the vertical shift of 5 units.  

Start by solving for the y-intercept. The y-intercept is the value of y (or g(x) when x (or f(x) )  = 0:

Substitute f(x) with 0:

g(x) = f(x) + 5

g(x) = 0 + 5

g(x) = 5

The y-intercept is (0, 5)

According to one of the hints provided in your instruction, it states that you can use the slope to find another point.  

In your given function, g(x) = f(x) + 5, the slope is 1 (it is implied, meaning, if your function is rewritten in its slope-intercept form, it is y = x + 5, in which your slope is implied as 1/1 or 1). So, to find another point, from the y-intercept (0, 5), you can go 1 unit up, and 1 unit to the right, which gives you the next point: (1, 6). Likewise, to go to the opposite direction, you can go down 1 unit, and 1 unit to the left.  

 

2.  h(x) = 2 * f(x) - 3

The slope of this function is 2, and the y-intercept is -3.  If you rewrite h(x) = 2 * f(x) - 3 into its slope-intercept form, it will be: y = 2x - 3. That is why the slope (m) = 2, and the y-intercept (b) = -3.  

To start, we can find the y-intercept, which is, again, the value of y (or h(x)) when f(x) = 0:

h(x) = 2 * 0 - 3

h(x) = 0 - 3

h(x) = -3

Therefore, the y-intercept is (0, -3). This can be your starting point to draw a line.  

From this point, you can use the slope (2/1) to find more points by going up 2 units, and 1 unit to the right. You'll end up with the next point, (1, -1).  Likewise, to go on the opposite direction, you can go 2 units down, and 1 unit to the left.  

3. j(x) = ½* f(x) - 1

The slope of this function is 1/2, and the y-intercept is -1. If you rewrite j(x) = ½* f(x) - 1 into its slope-intercept form, it will be: y = 1/2x - 1. That is why the slope (m) = ½, and the y-intercept (b) = -1.  

Same as the previous steps, you can start with the y-intercept by setting f(x) = 0:

j(x) = ½* f(x) - 1

j(x) = ½* 0 - 1

j(x) = 0 - 1

j(x) = - 1

Therefore, the y-intercept is (0, -1). Same as the previous functions, you can use the slope (m = ½) and start going 1 unit up, and 2 units to the right to get to the next point, (2, 0).  Keep going until you have enough points to connect and draw a line with.

Please see the attached image for the graph.