Analyze the effect of the graph from k(x)=4.82x+3−−−−−√−4

Question

𝑘
(
𝑥
)
=
4.8
2
𝑥
+
3
−
4
to m(x)=1.22x+3−−−−−√−4
𝑚
(
𝑥
)
=
1.2
2
𝑥
+
3
−
4

(1 point)
Responses

There is a vertical stretch by a factor of 4.
There is a vertical stretch by a factor of 4.

There is a vertical compression by a factor of 3.6.
There is a vertical compression by a factor of 3.6.

There is a vertical compression by a factor of 4.
There is a vertical compression by a factor of 4.

There is a vertical compression by a factor of 14
1
4
.

Answer 1

To analyze the effect of the transformation from the function \( k(x) = \sqrt{4.82x + 3} - 4 \) to \( m(x) = \sqrt{1.22x + 3} - 4 \), we need to focus on the coefficients of \( x \) within the square root.

The square root function has a general form of \( \sqrt{ax + b} \), and we can determine whether it's a stretch or compression based on the value of \( a \).

1. For \( k(x) \):

   • The coefficient of \( x \) is \( 4.82 \).

2. For \( m(x) \):

   • The coefficient of \( x \) is \( 1.22 \).

To see the effect of this change, we consider how these coefficients affect the vertical aspects of the graph:

• If \( a > 1 \), the graph is vertically compressed by a factor of \( 1/a \).
• If \( 0 < a < 1 \), the graph is vertically stretched.

Now comparing \( k(x) \) to \( m(x) \):

\[ \text{Factor of Compression} = \frac{4.82}{1.22} \approx 3.95 \]

So, since \( 1.22 < 4.82 \), it indicates that the graph of \( m(x) \) is vertically compressed compared to the graph of \( k(x) \).

Hence, we can conclude:

There is a vertical compression by a factor of approximately \( 4 \).

Therefore, the closest response is:

There is a vertical compression by a factor of 4.