Math

QuestionSketch the graphs of f(x)=x2f(x)=x^{2} and g(x)=18x2g(x)=\frac{1}{8} x^{2}. Find the points of g(x)g(x) corresponding to (1,1),(0,0),(1,1)(-1,1),(0,0),(1,1).

Studdy Solution

STEP 1

Assumptions1. The functions are f(x)=xf(x)=x^{} and g(x)=18xg(x)=\frac{1}{8} x^{} . The points given are (1,1),(0,0)(-1,1),(0,0), and (1,1)(1,1) of f(x)f(x)3. We need to find the corresponding points of these on g(x)g(x)

STEP 2

First, let's understand the relation between f(x)f(x) and g(x)g(x). We can see that g(x)g(x) is f(x)f(x) scaled down by a factor of 18\frac{1}{8}.

STEP 3

So, to find the corresponding points on g(x)g(x), we need to scale down the y-coordinate of the points on f(x)f(x) by a factor of 18\frac{1}{8}.

STEP 4

Let's start with the first point (1,1)(-1,1) on f(x)f(x). The x-coordinate remains the same, and the y-coordinate becomes 18\frac{1}{8} times the original y-coordinate.
g(1)=18×f(1)=18×1=18g(-1) = \frac{1}{8} \times f(-1) = \frac{1}{8} \times1 = \frac{1}{8}So, the corresponding point on g(x)g(x) is (1,18)(-1,\frac{1}{8}).

STEP 5

Next, let's find the corresponding point for (0,0)(0,0) on f(x)f(x).
g(0)=18×f(0)=18×0=0g(0) = \frac{1}{8} \times f(0) = \frac{1}{8} \times0 =0So, the corresponding point on g(x)g(x) is (0,0)(0,0).

STEP 6

Finally, let's find the corresponding point for (1,1)(1,1) on f(x)f(x).
g(1)=18×f(1)=18×1=18g(1) = \frac{1}{8} \times f(1) = \frac{1}{8} \times1 = \frac{1}{8}So, the corresponding point on g(x)g(x) is (1,18)(1,\frac{1}{8}).
The points (1,1),(0,0)(-1,1),(0,0), and (1,1)(1,1) of f(x)f(x) translate to the points (1,18),(0,0)(-1,\frac{1}{8}),(0,0), and (1,18)(1,\frac{1}{8}) of g(x)g(x).

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord