Mathematics Extension 1 Year 11 2023 Assessment Task 1

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For which value of $x$ is the function $f^{-1}(x)$ not defined?

0

5 (correct)

1

-1

Which pair of equations is NOT a parametric form of $y = mx + c$?

$x = 2t + 3, y = 2mx - 3m + c$ (correct)

$x = t + 1, y = mx + m + c$

$x = t - 3, y = mx + c - 3m$

$x = t, y = mx + c$

What is the solution to the inequality $x^2 - 3x < 5$?

$x > 2$

$x < -2$

$-1 < x < 5$ (correct)

$x > 5$

Which inequality is equivalent to $2 eq 3x - 4$?

$x eq -2$ Signup and view all the answers

What is the solution to $|3x - 1| + 2 < 7$?

$0 < x < 2$ Signup and view all the answers

What is the largest domain containing $x = 5$ for which the inverse of $y = x^2 - 2$ is a function?

$[0, fty)$ Signup and view all the answers

Which of the following is true about the inverse of a many-to-one function?

It is one-to-one Signup and view all the answers

If the graph of 𝑦 = 𝑓(𝑥) passes through (1, 4), (3, 1), and (4, -1), what points does the graph of 𝑦^2 = 𝑓(𝑥) pass through?

(1, -2), (1, 2), (3, 1), and (3, -1) Signup and view all the answers

Which pair of equations is NOT a parametric form of 𝑦 = (2𝑥−3)^2?

𝑥 = 𝑡; 𝑦 = 4𝑡^2 − 12𝑡 + 9 Signup and view all the answers

For which value of 𝑥 is the function 𝑓(𝑥) = 𝑥 + 1 not defined and has a zero?

𝑥 = -1 Signup and view all the answers

In the context of functions, what does it mean if a function is many-to-one?

Each output value corresponds to multiple input values Signup and view all the answers

If a function is one-to-many, what does this imply?

Each input value has multiple corresponding output values Signup and view all the answers

What is the domain of $f^{-1}(x)$?

$x \leq -5$ Signup and view all the answers

What is the inverse of $y = (x - 2)^3 - 5$ in terms of $y$?

$y^{1/3} + 2$ Signup and view all the answers

What is the value of $t$ that gives the minimum value of $y$, in the parametric equations given?

$t = 1$ Signup and view all the answers

What is the Cartesian equation of the parabola defined by the parametric equations?

$y = a(x-1)^2 + k$ Signup and view all the answers

In the graph of $y = f(x)$, if $(a,b)$ and $(c,d)$ are points on the curve, what does sketching $y = f(|x|)$ involve?

Reflecting the curve over both axes Signup and view all the answers

For the equation $-b \pm \sqrt{b^2 - 4ac}$, what does it represent when $a,b,c,x$ are plugged in?

The solutions of a quadratic equation Signup and view all the answers