You must be logged in to see worked solutions.

Already have an account? Log in here.

Graphs are visual representations of functions. If you know how to read graphs, you can say a lot about a function just by looking at its graph. Learn this fine art of mathematical divining.

In the above diagram, suppose the equation of curve **A** is \(y=ax^2.\) Which of the following is a possible equation for curve **B**?
\[\begin{align}
\text{(i) } y&=5ax^2 &\qquad \text{(ii) } y&=-2ax^2 \\
\text{(iii) } y&=6ax^2 &\qquad \text{(iv) } y&=-\frac{1}{2}ax^2
\end{align}\]

You must be logged in to see worked solutions.

Already have an account? Log in here.

In the above diagram, **A** is a circle with radius \(2\) centered at the origin and **B** is an ellipse with major axis \(4\) and minor axis \(2\) centered at \((7, 5).\) If **B** is stretched and translated to obtain **A**, which of the following processes should be applied?

(i) Translate **B** by \(-7\) and \(-5\) in the positive directions of the \(x\)-axis and \(y\)-axis, respectively, and stretch by a factor of \(2\) with respect to the \(y\)-axis.

(ii) Translate **B** by \(-7\) and \(-5\) in the positive directions of the \(x\)-axis and \(y\)-axis, respectively, and stretch by a factor of \(2\) with respect to the \(x\)-axis.

(iii) Translate **B** by \(7\) and \(5\) in the positive directions of the \(x\)-axis and \(y\)-axis, respectively, and stretch by a factor of \(\frac{1}{2}\) with respect to the \(y\)-axis.

(iv) Translate **B** by \(-7\) and \(-5\) in the positive directions of the \(x\)-axis and \(y\)-axis, respectively, and stretch by a factor of \(\frac{1}{2}\) with respect to the \(x\)-axis.

You must be logged in to see worked solutions.

Already have an account? Log in here.

You must be logged in to see worked solutions.

Already have an account? Log in here.

Given the graph \( y = \ln x \), which of these statements describes the transformations to get the graph of \( y = \ln (4x^2 + 4x + 1) \) for \( x > - \frac{1}{2} \)?

\(\quad \text{(1)}\) Translate to the left by 1 and up by \( \ln 4 \), then scale vertically by 2.

\(\quad \text{(2)}\) Translate to the left by \(\frac{1}{2}\) and up by \( \ln 2 \), then scale vertically by 2.

\(\quad \text{(3)}\) Translate to the left by 1 and up by \( \ln 2 \), then scale vertically by 2.

\(\quad \text{(4)}\) Translate to the left by \( \frac{1}{2} \) and up by \( \ln 4 \), then scale vertically by 2.

You must be logged in to see worked solutions.

Already have an account? Log in here.

Given the graph \( y = 7x^2+7 \), what is the sequence of operations required to obtain the graph of \[ y = 175x^2 +3?\]

**Note:** The above graph is not drawn to scale.

(i) Stretch the given graph by a factor of \(5\) with respect to the \(x\)-axis and translate by \(4\) in the positive direction of the \(x\)-axis.

(ii) Stretch the given graph by a factor of \(5\) with respect to the \(y\)-axis and translate by \(-4\) in the positive direction of the \(y\)-axis.

(iii) Stretch the given graph by a factor of \(\frac{1}{5}\) with respect to the \(x\)-axis and translate by \(4\) in the positive direction of the \(y\)-axis.

(iv) Stretch the given graph by a factor of \(\frac{1}{5}\) with respect to the \(x\)-axis and translate by \(-4\) in the positive direction of the \(y\)-axis.

You must be logged in to see worked solutions.

Already have an account? Log in here.

×

Problem Loading...

Note Loading...

Set Loading...